
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 $f(x)=\sin (\pi-\omega x)\cos \omega x+\cos ^{2}\omega x$ $(\omega > 0)$ has the smallest positive period of $\pi$.

(1) Find the value of $\omega$;

(2) By shrinking the x-coordinates of the points on the graph of the function $y=f(x)$ to half of their original values while keeping the y-coordinates unchanged, we obtain the graph of the function $y=g(x)$. Find the minimum value of the function $g(x)$ in the interval $[0,16\pi]$.

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