
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 $f(\alpha)=\dfrac{\sin(\alpha-\dfrac{\pi}{2})\cos(\dfrac{3\pi}{2}-\alpha)\tan(\pi+\alpha)\cos(\dfrac{\pi}{2}+\alpha)}{\sin(2\pi-\alpha)\tan(-\alpha-\pi)\sin(-\alpha-\pi)}$.

(1) Simplify $f(\alpha)$;

(2) If $\alpha=-\dfrac{31\pi}{3}$, find the value of $f(\alpha)$.

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