
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 that $\alpha$ is an angle in the third quadrant, and $f(\alpha) = \frac{\sin \left( \alpha - \frac{\pi}{2} \right) \cos \left( \frac{3\pi}{2} + \alpha \right) \tan \left( \pi - \alpha \right)}{\tan \left( -\alpha - \pi \right) \sin \left( -\alpha - \pi \right)}$.

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

(2) If $\cos \left( \alpha - \frac{3\pi}{2} \right) = \frac{1}{5}$, find the value of $f(\alpha)$.

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