
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 $f(\alpha) = \frac{\tan(\pi + \alpha)\sin(2\pi - \alpha)\cos(\pi - \alpha)}{\sin(\alpha + \frac{3}{2}\pi)\cos(\alpha - \frac{3}{2}\pi)}$,

(1) Simplify $f(\alpha)$;

(2) If $\sin \alpha = -\frac{2}{3}$, $\alpha \in [-\pi, -\frac{\pi}{2}]$, find the value of $f(\alpha)$.

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