
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 $f(\alpha) = \frac {\sin(4\pi-\alpha)\cos(\pi-\alpha)\cos\left( \frac {3\pi}{2}+\alpha\right)\cos\left( \frac {7\pi}{2}-\alpha\right)}{\cos(\pi +\alpha )\sin(2\pi -\alpha )\sin(\pi +\alpha )\sin\left( \frac {9\pi}{2}-\alpha \right)}$,
(1) Simplify $f(\alpha)$.
(2) Find $f\left(- \frac {31}{6}\pi\right)$.

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