
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 ABC be an acute triangle with AB = 3 and AC = 4. Suppose that AH, AO, and AM are the altitude, the bisector and the median derived from A, respectively. If HO = 3MO, then find the length of BC.

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