
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 $f(x) = -x^2 + 2x\tan\theta + 1$, where $x \in [-\sqrt{3}, 1]$ and $\theta \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

(1) When $\theta = -\frac{\pi}{4}$, find the maximum and minimum values of the function $f(x)$.

(2) Determine the range of values for $\theta$ such that $y = f(x)$ is a monotonic function on the interval $[-\sqrt{3}, 1]$.

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