
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 differentiable function $f(x)$ defined on $\mathbb{R}$ with its derivative denoted as $f'(x)$, the function satisfies the equation $f(x) + f(2 - x) = (x - 1)^2$, and when $x \leqslant 1$, it holds that $f'(x) + 2 < x$. If $f(m) - f(1 - m) \geqslant \frac{3}{2} - 3m$, determine the range of the real number $m$.

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