
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 $\triangle ABC$, $AB = 12$, $BC = 15$, $CA = 13$. Point $M$ is the midpoint of $AB$ and point $H$ is the foot of the altitude from vertex $A$ to side $BC$. Find the length of segment $HM$.
A) 0.5
B) 1
C) 1.5
D) 2
E) 2.5

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