
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 parabola with the equation $x^{2}=2py$ ($p > 0$), where the distance between the vertex and focus is equal to the diameter of a circle with an area of $4π$. A line $L$ passing through the point $(-1,0)$ intersects the parabola at only one point. Determine the distance from the focus to line $L$.

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