
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 P be a moving point on the parabola C: y²=4x, and Q be a moving point on the axis of symmetry of C. Find the range of the minimum value of the distance from P to the line passing through Q and perpendicular to OQ (O is the origin of the coordinate system).

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