
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
Circle  $\omega$  lies inside the circle  $\Omega$  and touches it internally at point  $P$ . Point  $S$  is taken on  $\omega$  and the tangent to  $\omega$  is drawn through it. This tangent meets  $\Omega$  at points  $A$  and  $B$ . Let  $I$  be the centre of  $\omega$ . Find the locus of circumcentres of triangles  $AIB$ .
 

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