
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
If the function
$$
f(x) = 3 \cos \left(\omega x + \frac{\pi}{6}\right) - \sin \left(\omega x - \frac{\pi}{3}\right) \quad (\omega > 0)
$$
has a minimum positive period of \(\pi\), then the maximum value of \(f(x)\) on the interval \(\left[0, \frac{\pi}{2}\right]\) is \(\qquad\)

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