
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
The line $l$ passing through the point $(3, 0)$ intersects with the circle defined by $x^2 + y^2 + x - 6y + 3 = 0$ at points $P$ and $Q$, and $\overline{OP}$ is perpendicular to $\overline{OQ}$ (where $O$ is the origin). Find the equation of the line $l$.

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