
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  $\triangle XOY$  be a right-angled triangle with  $\angle XOY=90^\circ$ .  Let  $M$  and  $N$  be the midpoints of legs  $OX$  and  $OY$ , respectively.  Find the length  $XY$  given that  $XN=22$  and  $YM=31$ .

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