
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 acute angles \( \alpha \) and \( \beta \) satisfy
\[ \sin \beta = m \cos (\alpha + \beta) \cdot \sin \alpha \quad (m > 0, \alpha + \beta \neq \frac{\pi}{2}) \]
let \( x = \tan \alpha \) and \( y = \tan \beta \).

(1) Find the expression of \( y = f(x) \);

(2) Under the condition in (1), determine the maximum value of the function \( y \) when \( \alpha \in \left[\frac{\pi}{4}, \frac{\pi}{2}\right) \).

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