
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 $$f(x)=\cos^{2}\omega x- \sqrt {3}\sin\omega x\cdot \cos\omega x$$ (where $\omega>0$), the smallest positive period is $\pi$,
(1) Find the intervals of monotonic increase and the center of symmetry for the function $f(x)$;
(2) If $A$ is an acute angle of the triangle $\triangle ABC$, find the range of values for $f(A)$.

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