
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 vectors $\overrightarrow{m}=(\cos 2x, \frac{\sqrt{3}}{2}\sin x - \frac{1}{2}\cos x)$ and $\overrightarrow{n}=(1, \frac{\sqrt{3}}{2}\sin x - \frac{1}{2}\cos x)$, let the function $f(x) = \overrightarrow{m} \cdot \overrightarrow{n}$.

1. Find the set of values of $x$ for which the function $f(x)$ attains its maximum value.
2. Let $A$, $B$, and $C$ be the three internal 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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