
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 that function f(x) is an even function defined on R, let g(x) = f(x) - x², and function g(x) is an increasing function on the interval [0, +∞). Determine the solution set for the inequality f(x+2) - f(2) > x² + 4x.

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