
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 an acute triangle $\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively, if $c\cos A$, $b\cos B$, and $a\cos C$ form an arithmetic sequence.
(I) Find the value of angle $B$.
(II) Consider the function $f(x)=\sqrt{3}\sin \omega x\cos \omega x-\frac{1}{2}\cos 2\omega x (\omega > 0)$, and the distance between two adjacent highest points on the graph of $f(x)$ is $\pi$. Find the range of values for $f(A)$.

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