math mode $$ makes line too long inside itemize environment

Question

I have a list of items as follows:

\begin{itemize}
\item define \textit{N} to be the largest non-negative integer such that $k\times 4^{H-1}<max(f(X(t);4,3), f(X(t);5,7))$. If $f(X(t);0,-1)>k\times 4^{H-1}$ and blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla blablabla.
\end{itemize}

The problem is that the first line is too long (see picture=. How can I make the expression inside the math mode naturally go into the next line as if it was text?

My preamble

%\UseRawInputEncoding
\documentclass[12pt]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\usepackage{titlesec}
%\titleformat{\section}
% {\normalfont\fontsize{12}{15}\bfseries}{\thesection}{1em}{}
% \usepackage{titlesec}
%\titleformat{\subsection}
% {\normalfont\fontsize{12}{15}\bfseries}{\thesubsection}{1em}{}
\usepackage{amsmath,amsfonts,amssymb}
\newcommand*{\defeq}{\stackrel{\text{def}}{=}}
\usepackage{color,xcolor}
\usepackage{subfig} 
\usepackage[pdftex]{graphicx}
\usepackage{setspace}
\usepackage{booktabs}
\usepackage{lscape,url}
\usepackage[round]{natbib}
\usepackage{lipsum}
\usepackage[hidelinks]{hyperref}
\usepackage[labelfont={bf},labelsep=colon,justification=justified]{caption}
\usepackage{array}
\newcolumntype{P}[1]{>{\centering\arraybackslash}p{#1}}
\newcolumntype{L}[1]{>{ \arraybackslash}p{#1}}
\usepackage{eurosym}
\usepackage{titlesec}
\usepackage{rotating}
\usepackage{longtable}
\usepackage{placeins}
\usepackage{bookmark}
\usepackage[english]{babel}
\usepackage[autostyle, english = american]{csquotes}
\usepackage{indentfirst}
%\usepackage[multiple]{footmisc}
%\usepackage{appendix}
\usepackage[top=1.5in, bottom=1.5in, left=0.9in, right=0.9in]{geometry}
\topmargin -1.5cm
\oddsidemargin -0.04cm
\evensidemargin -0.04cm
\textwidth 16.59cm
\textheight 21.94cm
\usepackage[font=footnotesize,labelfont=bf]{caption}
\usepackage{threeparttable}
\setcounter{MaxMatrixCols}{10}
\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\renewcommand{\baselinestretch}{2}
\newcommand\cites[1]{\citeauthor{#1}'s\ (\citeyear{#1})}
\usepackage{setspace}
\usepackage{hyperref}
\usepackage{comment}
\usepackage{multirow}
\usepackage{textcomp}
\interfootnotelinepenalty=10000
\usepackage[bottom]{footmisc}
\usepackage[labelsep=period]{caption}
\usepackage{lscape} 
\usepackage{blindtext}
\usepackage{dcolumn}
\usepackage{capt-of}
\newcolumntype{d}[1]{D{.}{.}{#1}}
%\usepackage{siunitx}
%\usepackage{mathptmx,siunitx}
%\sisetup{input-symbols = {()},  % do not treat "(" and ")" in any special way
  %       group-digits  = false} % no grouping of digits
\usepackage{tablefootnote}
\setlength{\footskip}{65pt}
\onehalfspacing
%\usepackage{etoolbox}
%\usepackage{xr}
%\externaldocument[SND-]{NetworkDescription}
\usepackage{titlesec}
\makeatletter
\newcommand{\setappendix}{Appendix~\thechapter:~}
\newcommand{\setchapter}{\thechapter~}
\titleformat{\chapter}{\bfseries\LARGE}{%
  \ifnum\pdfstrcmp{\@currenvir}{appendices}=0
    \setappendix
  \else
    \setchapter
  \fi}{0em}{}
\makeatother
\usepackage[titletoc]{appendix}
\usepackage[T1]{fontenc}
\usepackage{etoolbox}
\makeatletter
\patchcmd{\@maketitle}{\LARGE}{\fontsize{16}{17}\selectfont}{}{}
\makeatother
\begin{document}

Answer 1

I would suggest rephrasing the sentence and offer the following example for your reference.

\begin{itemize}
\item define $k\times 4^{N-1}<\max(f(X(t);4,3), f(X(t);5,7))$ with \textit{N} being the largest non-negative integer. If $f(X(t);0,-1)>k\times 4^{H-1}$ and \ldots
\end{itemize}

Answer 2

I've simplified your lengthy preamble to what I believe is the bare minimum needed to reproduce the formating issue you're looking to fix.

Basically, TeX does not like to allow line breaks in inline math, including right after commas. To enable a line break at a specific point, insert an \allowbreak directive as needed.

\documentclass[12pt]{article}
\textwidth 16.59cm
\oddsidemargin -0.04cm
\evensidemargin -0.04cm
\usepackage[T1]{fontenc}

\begin{document}
\begin{itemize}
\item Define $N$ to be the largest non-negative integer such that 
$k\times 4^{H-1}<\max(f(X(t);4,3), f(X(t);5,7))$. 
If $f(X(t);0,-1)>k\times 4^{H-1}$ and blablabla 
blablabla blablabla blablabla blablabla.

\item Define $N$ to be the largest non-negative integer such that 
$k\times 4^{H-1}<\max(f(X(t);4,3),\allowbreak f(X(t);5,7))$. 
If $f(X(t);0,-1)>k\times 4^{H-1}$ and blablabla 
blablabla blablabla blablabla blablabla.
\end{itemize}
\end{document}