
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 $0 < \varphi < \pi$, and it satisfies $\sin(\varphi + \frac{\pi}{4}) = \sin(\varphi - \frac{\pi}{4})$, let the function $f(x) = \sin(2x + \frac{\varphi}{2})$.
(1) Find the value of $\varphi$;
(2) Let $\frac{\pi}{4} < \alpha < \frac{\pi}{2}$, and $f(\alpha) = -\frac{5}{13}$, find the value of $\sin 2\alpha$.

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