
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) = x² + 4[sin(θ + $\frac{π}{3}$)]x - 2, where θ ∈ [0, 2π).
1. If function f(x) is an even function, find the value of tanθ.
2. If f(x) is a monotonic function on [-$\sqrt{3}$, 1], find the range of θ.

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