
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 $f(\alpha) = \frac{\sin(\pi-\alpha)\cos(2\pi-\alpha)\tan(-\alpha+ \frac{3\pi}{2})\tan(-\alpha-\pi)}{\sin(-\pi -\alpha)}$.
1. Simplify $f(\alpha)$;
2. If $\alpha$ is an angle in the third quadrant, and $\cos\left(\alpha- \frac{3\pi}{2}\right) = \frac{1}{5}$, find the value of $f(\alpha)$;
3. If $\alpha = -1860^\circ$, find the value of $f(\alpha)$.

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