
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 $$f(\alpha)= \frac{\sin(\alpha-\pi)\cos\left(\frac{3\pi}{2}+\alpha\right)\tan(-\alpha-\pi)}{\sin(5\pi+\alpha)\tan^2(-\alpha-2\pi)}$$  
(1) Simplify $f(\alpha)$;  
(2) If $\alpha$ is an angle in the third quadrant, and $$\cos\left(\alpha+\frac{\pi}{2}\right)=\frac{1}{5}$$, find the value of $f(\alpha+\pi)$;  
(3) If $$\alpha=\frac{2011\pi}{3}$$, find the value of $f(\alpha)$.

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