
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
(1) Given $\tan\alpha=3$, calculate $$\frac {3\sin\alpha+\cos\alpha}{\sin\alpha-2\cos\alpha}$$  
(2) Simplify: $$\frac {-\sin(\pi+\alpha)+\sin(-\alpha)-\tan(2\pi+\alpha)}{\tan(\alpha+\pi)+\cos(-\alpha)+\cos(\pi-\alpha)}$$  
(3) Given $$\sin\alpha+\cos\alpha= \frac {1}{2} (0<\alpha<\pi)$$, find $\sin\alpha\cos\alpha$.

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