
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
Let the function $f(x) = 3\cos\left(\frac{3\pi}{2} + 2\omega x\right) + \sin\left(2\omega x - \pi\right) + 1$, where $\omega > 0$.
1. If $\omega = 1$, and $f(x + \theta)$ is an even function, find the minimum value of $\theta$.
2. If $\omega = 1$ and there exists $x \in \left[\frac{\pi}{12}, \frac{\pi}{3}\right]$ such that $(f(x) - 1)^2 - (f(x) - 1)m + 3 \leq 0$ holds, find the range of values for $m$.
3. If $y = f(x) - 1$ has at least 2016 local extrema in the interval $x \in (0, 2015)$, find the range for $\omega$.

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