
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
Let the function $f(x) = \sin(\omega x - \frac{3\pi}{4})$ ($\omega > 0$) have a minimum positive period of $\pi$.

(1) Find $\omega$;  
(2) If $f\left(\frac{\alpha}{2} + \frac{3\pi}{8}\right) = \frac{24}{25}$, and $\alpha \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, find the value of $\tan\alpha$.

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