
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 $f(x) = \sqrt{3}\sin \omega x + \cos \omega x (\omega > 0)$, the distance between two adjacent intersections of the graph of $y=f(x)$ and the line $y=-2$ is equal to $\pi$. Determine the interval of $f(x)$ where it is strictly increasing.

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