
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the function $f(x)=\cos (\omega x+\varphi)$ $(\omega > 0, 0 < \varphi < \frac{\pi}{2})$ has a minimum positive period of $\pi$, and $f\left( \frac{\pi}{3} \right)=-\frac{\sqrt{3}}{2}$.

$(1)$ Find the values of $\omega$ and $\varphi$;

$(2)$ If $f(x) > \frac{1}{2}$, find the range of $x$.

Present the answer in LaTex format: \boxed{Your answer}
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