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

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