
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 $f(x) = \sin^2x + \sqrt{3}\cos x \cos\left(\frac{\pi}{2} - x\right)$.

(I) Find the center of symmetry and the equation of the axis of symmetry of the function $f(x)$.

(II) When $x \in \left[0, \frac{7\pi}{12}\right]$, find the maximum and minimum values of the function $f(x)$.

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