
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
$$ f(\alpha)= \frac{\sin(7\pi-\alpha)\cdot \cos(\alpha+ \frac{3\pi}{2})\cdot \cos(3\pi+\alpha)}{\sin\left(\alpha - \frac{3\pi}{2}\right)\cdot \cos\left(\alpha + \frac{5\pi}{2}\right)\cdot \tan(\alpha -5\pi)} $$
(1) Simplify $f(\alpha)$.
(2) If $\alpha$ is in the second quadrant and $\cos\left( \frac{3\pi}{2}+\alpha\right)= \frac{1}{7}$, find the value of $f(\alpha)$.

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