
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
Let  $ABC$  be a triangle with  $\angle A = 60^o$ . Line  $\ell$  intersects segments  $AB$  and  $AC$  and splits triangle  $ABC$  into an equilateral triangle and a quadrilateral. Let  $X$  and  $Y$  be on  $\ell$  such that lines  $BX$  and  $CY$  are perpendicular to ℓ. Given that  $AB = 20$  and  $AC = 22$ , compute  $XY$  .

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