
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 \( ABC \), angle \( C \) is a right angle, and the altitude from \( C \) meets \( \overline{AB} \) at \( D \). The lengths of the sides of \( \triangle ABC \) are integers, \( BD=29^2 \), and \( \cos B = m/n \), where \( m \) and \( n \) are relatively prime positive integers. Find \( m+n \).

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