
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 $f(x)=\frac{5}{4}\cos^{2}x-\frac{\sqrt{3}}{2}\sin x\cos x-\frac{1}{4}\sin^{2}x$.
(I) Find the set of $x$ values when the function $f(x)$ reaches its maximum;
(II) Let $A$, $B$, and $C$ be the three interior angles of an acute triangle $ABC$. If $\cos B=\frac{3}{5}$ and $f(C)=-\frac{1}{4}$, find the value of $\sin A$.

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