
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 an equilateral triangle with side length  $2$ , and let  $M$  be the midpoint of  $\overline{BC}$ .  Points  $X$  and  $Y$  are placed on  $AB$  and  $AC$  respectively such that  $\triangle XMY$  is an isosceles right triangle with a right angle at  $M$ .  What is the length of  $\overline{XY}$ ?

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