
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 $\triangle ABC$, with $AB = 13$, $BC = 14$, and $CA = 15$, and where $M$ is the midpoint of side $AB$ and $H$ is the foot of the altitude from $A$ to $BC$, find the length of $HM$.

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