
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 the function $f(\alpha) = \frac{\sin(\pi + \alpha) \cos(2\pi - \alpha) \tan(-\alpha + \frac{3\pi}{2})}{\cos(-\pi - \alpha)}$, find the value of $f\left(-\frac{31\pi}{3}\right)$.

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