
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 $0 < \alpha < \frac{\pi}{2}$, and $\sin{\alpha} = \frac{4}{5}$,

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

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