
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
The function $y = \tan{\omega x}$ ($\omega > 0$) intersects with the line $y=a$ at points A and B, and the minimum value of $|AB|$ is $\pi$. Find the interval where the function $f(x) = \sqrt{3}\sin{\omega x} - \cos{\omega x}$ is monotonically increasing.

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