
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 O be the origin of coordinates, and let there be two points P and Q on the curve $x^2+y^2+2x-6y+1=0$, such that they are symmetric about the line $x+my+4=0$ and also 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}
user