
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
From any point \( P \) on the parabola \( y^2 = 2x \), a perpendicular is drawn to its directrix \( l \), and the foot of the perpendicular is \( Q \). The line connecting the vertex \( O \) and point \( P \) intersects the line connecting the focus \( F \) and point \( Q \) at point \( R \). What is the equation of the locus of point \( R \)?

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