
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, the function $f(\alpha)$ is defined as:
$$f(\alpha) = \frac {\sin(\alpha - \frac {\pi}{2}) \cdot \cos( \frac {3\pi}{2} + \alpha) \cdot \tan(\pi - \alpha)}{\tan(-\alpha - \pi) \cdot \sin(-\alpha - \pi)}.$$  
1. Simplify $f(\alpha)$.
2. If $\cos(\alpha - \frac {3\pi}{2}) = \frac {1}{5}$, find $f(\alpha + \frac {\pi}{6})$.

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