
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 circle C be defined by the equation $(x-3)^2 + (y-5)^2 = 5$. A line $l$ passes through the center of circle C and intersects the circle at points A and B, and intersects the y-axis at point P. If point A is exactly the midpoint of segment BP, then the equation of line $l$ is __________.

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