
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
Rectangle  $HOMF$  has  $HO=11$  and  $OM=5$ . Triangle  $ABC$  has orthocenter  $H$  and circumcenter  $O$ .  $M$  is the midpoint of  $BC$  and altitude  $AF$  meets  $BC$  at  $F$ . Find the length of  $BC$ .

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