
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
A line $l$ passing through the origin intersects the circle $x^2+y^2=1$ at points $P$ and $Q$. Point $A$ is the intersection of the circle and the negative semi-axis of the $x$-axis. The circle with $AQ$ as the diameter intersects line $l$ at point $N$, which is different from point $Q$. The product of the slopes of lines $AN$ and $AP$ is equal to 1. Determine the equation of line $l$.

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