
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 that the line passing through the focus \( F \) of the parabola \( y^2 = 4x \) intersects the parabola at points \( M \) and \( N \), and \( E(m,0) \) is a point on the x-axis, with the extensions of \( M E \) and \( N E \) intersecting the parabola again at points \( P \) and \( Q \) respectively. If the slopes \( k_1 \) and \( k_2 \) of the lines \( M N \) and \( P Q \) satisfy \( k_1 = 3k_2 \), find the value of the real number \( m \).

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