
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
Triangle  $ABC$  has  $AB=25$ ,  $AC=29$ , and  $BC=36$ .  Additionally,  $\Omega$  and  $\omega$  are the circumcircle and incircle of  $\triangle ABC$ .  Point  $D$  is situated on  $\Omega$  such that  $AD$  is a diameter of  $\Omega$ , and line  $AD$  intersects  $\omega$  in two distinct points  $X$  and  $Y$ .  Compute  $XY^2$ .

*Proposed by David Altizio*

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