
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 a circle C: $(x-3)^2+(y-3)^2=9$ and a point P(5, -1) outside the circle.  
(1) Point A is any point on circle C, find the equation of the trajectory of the midpoint Q of PA;  
(2) Draw a line l through P, if there are exactly three points on circle C that are at a distance of 1 from line l, find the equation of line l.

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