
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 $f(x) = -\sin^2x + a\sin x + b\cos x$ is an even function, and $f(\pi) = -1$,  
(1) Find $f(x)$;  
(2) Given $\theta \in (0, \frac{\pi}{2})$, and $\tan \theta = \sqrt{2}$, if for any $x \in \left[-\frac{\pi}{2}, 0\right]$, the inequality $a \leq f(2x+\theta) + m \leq 4b$ always holds, find the range of values for $m$.

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