
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
A function $f(x)$ defined on $\mathbb{R}$ satisfies: $f(x) + f(-x) = \frac{x^2}{2}$ for any $x \in \mathbb{R}$, and $2f'(x) > x$ on the interval $[0, +\infty)$. If $f(a) - f(2-a) \geq a - 1$, find the range of values for the real number $a$.

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