
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 that point $O$ is the coordinate origin, and there are two points $P$ and $Q$ on the curve $x^{2}+y^{2}+2x-6y+1=0$. These points are symmetric with respect to the line $x+my+4=0$ and satisfy $\overrightarrow{OP} \cdot \overrightarrow{OQ}=0$.

1. Find the value of $m$.
2. Find the equation of the line $PQ$.

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