
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 length 10, 11, and 13, point $H$ is the orthocenter. If $AD$ is the altitude to the side of length 11, find the ratio $HD:HA$, where $D$ and $A$ are as previously defined with $A$ opposite the side of length 11.
A) 0:1
B) 1:2
C) 2:3
D) 1:3
E) 1:4

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