
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 $\tan (\frac{\pi}{4} + \alpha) = 3$, compute:
(1) $\tan \alpha$;
(2) $\tan 2\alpha$;
(3) $\frac{2\sin \alpha\cos \alpha + 3\cos 2\alpha}{5\cos 2\alpha - 3\sin 2\alpha}$.

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