
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 \( y = \tan(\omega x) \) intersects the line \( y = a \) at points \( A \) and \( B \), and the minimum value of \( |A B| \) is \(\pi\). Determine the interval in which the function \( f(x) = \sqrt{3} \sin(\omega x) - \cos(\omega x) \) is increasing.

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