
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 parabola $x^2 = 4y$ have its focus at $F$. Draw a line $l$ with slope $k(k > 0)$ through point $F$ such that it intersects the parabola at points $A$ and $B$. Let point $P$ be the midpoint of segment $AB$. Drawing a perpendicular from $P$ to the $x$-axis, it intersects the parabola at point $M$. If $|MF| = 4$, find the equation of line $l$.

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