
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
In triangle  $ABC$ , let  $M$  be the midpoint of  $BC$ ,  $H$  be the orthocenter, and  $O$  be the circumcenter. Let  $N$  be the reflection of  $M$  over  $H$ . Suppose that  $OA = ON = 11$  and  $OH = 7.$  Compute  $BC^2$ .

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