16. Given that the function $f(x) = 2\cos(\omega x + \varphi)$ has a partial graph as shown in the figure, then the minimum positive integer $x$ satisfying the condition $\left(f(x) - f\left(-\frac{7\pi}{4}\right)\right)\left(f(x) - f\left(\frac{4\pi}{3}\right)\right) > 0$ is $\_\_\_\_$.
III. Solution Questions (70 points total. Show all work, proofs, and calculations. Questions 17-21 are required for all students. Questions 22-23 are optional; students should answer according to requirements.)
16. Given that the function $f(x) = 2\cos(\omega x + \varphi)$ has a partial graph as shown in the figure, then the minimum positive integer $x$ satisfying the condition $\left(f(x) - f\left(-\frac{7\pi}{4}\right)\right)\left(f(x) - f\left(\frac{4\pi}{3}\right)\right) > 0$ is $\_\_\_\_$.
\section*{III. Solution Questions (70 points total. Show all work, proofs, and calculations. Questions 17-21 are required for all students. Questions 22-23 are optional; students should answer according to requirements.)}