
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
The circle  $x^2 + y^2 = 25$  intersects the abscissa in points  $A$  and  $B$ . Let  $P$  be a point that lies on the line  $x = 11$ ,  $C$  is the intersection point of this line with the  $Ox$  axis, and the point  $Q$  is the intersection point of  $AP$  with the given circle. It turned out that the area of the triangle  $AQB$  is four times smaller than the area of the triangle  $APC$ . Find the coordinates of  $Q$ .

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