
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]


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Given an even function f(x) defined on R, with its derivative denoted as f′(x). For x ≥ 0, it always holds that x/2*f'(x) + f(-x) ≤ 0. If g(x) = x^2*f(x), determine the solution set of the inequality g(x) < g(1-2x).

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