
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 \( f(x)=x^{2}+2x \cdot \tan \theta - 1 \) where \( x \in [-1, \sqrt{3}] \) and \( \theta \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \):
1. When \(\theta = -\frac{\pi}{6}\), 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 \([-1, \sqrt{3}]\).

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