
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 that the function $g(x)$ satisfies $g(x) = g'(1)e^{x-1} - g(0)x + \frac{1}{2}x^2$, and there exists a real number $x_0$ such that the inequality $2m - 1 \geq g(x_0)$ holds, determine the range of values for the real number $m$.

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