
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 $\cos (2\pi - \alpha) = -\frac {4}{5}$, and $\alpha$ is an angle in the third quadrant,
(1) find the value of $\cos\left(\frac {\pi}{2} + \alpha\right)$;
(2) find the value of $f(\alpha) = \frac {\tan (\pi - \alpha) \cdot \sin (\pi - \alpha) \cdot \sin \left(\frac {\pi}{2} - \alpha\right)}{\cos (\pi + \alpha)}$.

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