
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
Medians  $AM$  and  $BE$  of a triangle  $ABC$   intersect at  $O$ . The points  $O, M, E, C$  lie on one circle. Find the length of  $AB$  if  $BE = AM =3$ .

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