
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) Simplify $$\frac {\sin3\alpha}{\sin\alpha} - \frac {\cos3\alpha}{\cos\alpha}$$;  
(2) Given $\tan \frac {\alpha}{2} = 2$, find the value of $$\frac {6\sin\alpha+\cos\alpha}{3\sin\alpha-2\cos\alpha}$$.

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