
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 $8$, $15$, and $17$, the altitudes of the triangle meet at point $H$. If $AD$ is the altitude to the side of length $15$ from vertex $A$, calculate the ratio $HD:HA$.
A) 0
B) 1:2
C) 2:3
D) 1:4
E) 3:4

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