
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 the equation of circle C is $x^2+y^2+2x-6y-6=0$, and O is the origin of coordinates.  
(Ⅰ) Find the equation of the tangent line to circle C that passes through point M(-5, 11);  
(Ⅱ) If there are two points P, Q on circle C that are symmetric about the line $x+my+4=0$, and satisfy $\overrightarrow{OP} \cdot \overrightarrow{OQ} = -7$, find the value of $m$ and the equation of line PQ.

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