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

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