
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 $ \frac{\pi}{4} < \alpha < \frac{3\pi}{4} $ and $ 0 < \beta < \frac{\pi}{4} $, it is known that $ \cos\left(\frac{\pi}{4}+\alpha\right) = -\frac{4}{5} $ and $ \sin\left(\frac{3\pi}{4}+\beta\right) = \frac{12}{13} $.
1. Find the value of $\sin(\alpha + \beta)$.
2. Find the value of $\cos(\alpha - \beta)$.

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