
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) = 1 + 2sin(2x - π/3).
(1) Find the axis of symmetry and the center of symmetry.
(2) Find the maximum and minimum values of f(x) when x ∈ [π/4, π/2].
(3) If the inequality |f(x) - m| < 2 holds true for x ∈ [π/4, π/2], find the range of real number m.

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