
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
(1) Simplify the expression
$$
\frac {\sin(2\pi-\alpha) \cdot \tan(\pi-\alpha) \cdot \cos(-\pi+\alpha)}{\sin(5\pi+\alpha) \cdot \sin\left( \frac {\pi}{2}+\alpha\right)}
$$
(2) Find the maximum value of the function $f(x) = 2\cos x - \cos 2x$ and the corresponding values of $x$.

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