
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
Let point M$(x_1, f(x_1))$ and point N$(x_2, g(x_2))$ be on the graphs of the functions $f(x) = e^x - \frac{1}{2}x^2$ and $g(x) = x - 1$, respectively, with $x_1 \geq 0$, $x_2 > 0$. If line MN is parallel to the x-axis, then the minimum distance between points M and N is \_\_\_\_\_\_.

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