
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 $\triangle ABC$, $AB = 18$, $BC = 14$ and $CA = 15$. Point $M$ is on side $AB$ such that $AM = 3$ and $MB = 15$. Point $H$ is the foot of the altitude from $A$ to $BC$. Calculate the length of $HM$.

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