
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
ROMN is a rectangle with vertices in that order and RO = 11, OM = 5. The triangle ABC has circumcenter O and its altitudes intersect at R. M is the midpoint of BC, and AN is the altitude from A to BC. What is the length of BC?

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