
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 a function f(x) that has a derivative f'(x) for all real numbers x, and satisfies f(x) = 4x^2 - f(-x) for any real x. When x∈(-∞, 0), we have f'(x) + 1/2 < 4x. If f(m+1) ≤ f(-m) + 3m + 3/2, determine the range of the real number m.

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