
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 an acute-angled triangle \( ABC \), points \( D, E \), and \( F \) are the feet of the perpendiculars from \( A, B \), and \( C \) onto \( BC, AC \), and \( AB \), respectively. Suppose \(\sin A = \frac{3}{5}\) and \( BC = 39 \). Find the length of \( AH \), where \( H \) is the intersection of \( AD \) with \( BE \).

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