
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 line L has an inclination angle of 45° and intercepts the y-axis at 2. A point $P_0(2, y_0)$ on the parabola $y^2 = 2px$ (where $p > 0$) has a distance of 3 from its focus $F$. Let $M$ be a moving point on the parabola, find the minimum distance from $M$ to the line L.

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