
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 a triangle with sides of lengths 13, 14, and 15, the orthocenter is denoted by \( H \). The altitude from vertex \( A \) to the side of length 14 is \( A D \). Calculate the ratio \( \frac{H D}{H A} \).

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