
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 + $\frac{π}{4}$) (where A > 0, ω > 0) with an amplitude of 2 and a period of π.
1. Find the analytic expression of f(x) and write out the monotonically increasing interval of f(x).
2. First, shift the graph of f(x) to the left by $\frac{π}{4}$ units, then for each point, keep the vertical coordinate unchanged and change the horizontal coordinate to twice the original value, obtaining the graph of g(x). Find the analytic expression of g(x) and the center of symmetry (m, 0), where m ∈ [0, π].

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