
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 the parabola $x^2=4y$ with focus $F$, a line $l$ with slope $k$ ($k>0$) passes through point $F$ and intersects the parabola at points $A$ and $B$, with point $P$ being the midpoint of $AB$. A perpendicular line to the x-axis passing through point $P$ 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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