
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 orthocenter \( H \). Let \( D \) and \( E \) be the feet of the \( A \)- and \( B \)-altitudes, respectively. Given that \( AH = 20 \), \( HD = 15 \), and \( BE = 56 \), find the length of \( BH \).

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