
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 $f(x) = -2x^2 + 4mx - 1$  
(1) If $m=2$, $\theta \in (0, \frac{\pi}{2})$, find the maximum value of $\frac{f(\sin \theta)}{\sin \theta}$.  
(2) If for any $x \in [-1, 1]$, the maximum value of $y=f(x)$ is 7, find the value of $m$.

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