
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 focus of the parabola \( y^2 = 4x \) be \( F \). A line passing through point \( F \) intersects the parabola at points \( A \) and \( B \). Is there a line \( l \) such that for any point \( M \) on line \( l \), the slopes of lines \( MA \), \( MF \), and \( MB \) form an arithmetic sequence? If such a line exists, find the equation of line \( l \); if not, explain why.

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