
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
Choose one of the following three conditions to supplement the blank in the question below and answer it:
Given the function $y=2\sin(\omega x+\varphi)$ where $(A>0, \omega>0, 0<\varphi<\frac{\pi}{2})$, the distance between adjacent axes of symmetry on the graph of $f(x)$ is $\pi$, ____.
1. Find the expression of the function $f(x)$;
2. Find the intervals of monotonic increase of the function $f(x)$ on the interval $[0,2\pi]$.

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