
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
A circle with center at the origin and radius  $5$  intersects the abscissa in points  $A$  and  $B$ . Let  $P$   a point lying on the line  $x = 11$ , and the point  $Q$  is the intersection point of  $AP$  with this circle. We know what is the  $Q$  point is the midpoint of the  $AP$ . Find the coordinates of the point  $P$ .

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