
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 the function $$f(x) = \sin\left(\frac{5}{4}\pi -x\right) - \cos\left(\frac{\pi}{4} + x\right),$$
1. Find the interval where $f(x)$ is monotonically increasing.
2. Given $\cos(\alpha - \beta) = \frac{3}{5}$ and $\cos(\alpha + \beta) = -\frac{3}{5}$, where $0 < \alpha < \beta \leq \frac{\pi}{2}$, find $f(\beta)$.

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