
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 12, 13, and 17, the altitudes intersect at point \( H \). Let \( AD \) be the altitude to the side of length 13, with \( A \) being the vertex opposite the side of length 13. What is the ratio \( HD:HA \)?
A) \( \frac{25}{33} \)
B) \( \frac{13}{27} \)
C) 0
D) \( \frac{14}{15} \)

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