
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 $f(x) = \sin^2x + a\cos^2x$, where $a$ is a constant, $a \in \mathbb{R}$, and $f\left(\frac{\pi}{4}\right) = 0$.
(I) Find the minimum positive period of the function $f(x)$.
(II) Determine the maximum and minimum values of the function $f(x)$ when $x \in \left[\frac{\pi}{24}, \frac{11\pi}{24}\right]$.

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