
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
Altitudes \( BE \) and \( CF \) of acute triangle \( ABC \) intersect at \( H \). Suppose that the altitudes of triangle \( EHF \) concur on line \( BC \). If \( AB=3 \) and \( AC=4 \), then \( BC^2=\frac{a}{b} \), where \(a\) and \(b\) are relatively prime positive integers. Compute \(100a+b\).

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