
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 $f(\alpha) = \frac{\tan(\pi-\alpha) \cdot \cos(2\pi-\alpha) \cdot \sin(\frac{\pi}{2}+\alpha)}{\cos(-\alpha -\pi)}$.
1. Simplify $f(\alpha)$.
2. If $f(\alpha) = \frac{4}{5}$ and $\alpha$ is an angle in the second quadrant, find the value of $\cos(2\alpha+ \frac{\pi}{4})$.

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