
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 the line \( L: lx + my + n = 0 \) intersect the parabola \( y^2 = 4ax \) at points \( P \) and \( Q \). \( F \) is the focus of the parabola. The line segments \( PF \) and \( QF \) intersect the parabola at points \( R \) and \( S \). Determine the equation of the line \( RS \).

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