
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
Let the orthocenter of triangle $ABC$ be denoted by $M$. What is the distance from $M$ to side $BC$ if the length of the altitude from $A$ is $15 \mathrm{~cm}$ and $BC$ is divided into segments of $10 \mathrm{~cm}$ and $6 \mathrm{~cm}$?

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