
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 minimum distance from a point on the parabola $y^2 = 2px$ ($p > 0$) to its focus is 2, and a line $l$ passing through the point $(0,1)$ intersects the parabola at only one point, determine the distance from the focus to the line $l$.

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