
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 $\tan \frac{\alpha}{2} = 2$, find the value of  
$(1) \tan (\alpha + \frac{\pi}{4})$  
$(2) \frac{6\sin \alpha + \cos \alpha}{3\sin \alpha - 2\cos \alpha}$.

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