
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  $XOY$  be a triangle with  $\angle XOY = 90^o$ . Let  $M$  and  $N$  be the midpoints of legs  $OX$  and  $OY$ , respectively. Suppose that  $XN = 19$  and  $YM =22$ . What is  $XY$ ?

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