
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 that $\tan{\alpha} = 2$. Find:

1. The value of $\tan{(\alpha + \frac{\pi}{4})}$;
2. The value of $\frac{4\sin{\alpha} + 3\cos{(\pi - \alpha)}}{\sin{(\pi + \alpha)} + \cos{(-\alpha)}}$.

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