
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 $f\left(\alpha \right)=\frac{\mathrm{sin}\left(\pi -\alpha \right)\mathrm{cos}\left(2\pi -\alpha \right)\mathrm{cos}\left(-\alpha +\frac{3\pi }{2}\right)}{\mathrm{cos}\left(\frac{\pi }{2}-\alpha \right)\mathrm{sin}\left(-\pi -\alpha \right)}$.

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

(2) If $\alpha$ is an angle in the third quadrant and $\mathrm{cos}(\alpha -\frac{3\pi }{2})=\frac{1}{5}$, find the value of $f(\alpha )$.

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