
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) = sinωx, where ω > 0.
(1) If f(x) has a period of 4π, find ω and determine the solution set of f(x) = $\frac{1}{2}$.
(2) Given ω = 1, g(x) = f<sup>2</sup>(x) + $\sqrt{3}$f(-x)f($\frac{π}{2}$-x), where x ∈ [0, $\frac{π}{4}$], find the range of g(x).

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