
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 the parabola $y^2 = 4x$, a line $l$ is drawn through point A(1, 2) and intersects the parabola at another point B. Q is the midpoint of segment AB. A line $l_1$ is drawn through Q and is perpendicular to the y-axis, intersecting the parabola at point C. If point P satisfies $\overrightarrow{QC} = \overrightarrow{CP}$, then the minimum value of $|OP|$ is $\_\_\_\_\_\_$.

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