
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 $y^2 = 2px$ ($p > 0$), a line passing through its focus and having a slope of 1 intersects the parabola at points A and B. If the y-coordinate of the midpoint of segment AB is 2, then the equation of the directrix of this parabola is __________.

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