
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 $f(x)$, for any $x\in \mathbb{R}$, it satisfies $f(x) + f(-x) = x^{2}$. When $x\in [0,+\infty)$, ${f'}(x) - x - 1 < 0$. Determine the range of real number $a$ such that $f(2-a) \geq f(a) + 4 - 4a$.

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