
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) = A sin(ωx + φ) (where A > 0, ω > 0, 0 < φ < π/2), the distance between the adjacent axes of symmetry is π/2, and one of the highest points on the function graph is (π/12, 2).
1. Find the analytical expression of function f(x) and its monotonically increasing interval.
2. If x ∈ [0, π/4], find the maximum and minimum values of function f(x).

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