
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) = $\sqrt{3} \sin(\omega x + \phi)$ (where $\omega > 0$, $-\frac{\pi}{2} \leq \phi < \frac{\pi}{2}$), its graph is symmetric about the line x = $\frac{\pi}{3}$, and the distance between two adjacent highest points on the graph is $\pi$.

1. Find the expression for f(x) and its center of symmetry.
2. Find the interval where f(x) is strictly increasing.

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