
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 $ABC$, the sides $AB$ and $AC$ measure $6$ inches and $8$ inches, respectively. The median $AM$ from vertex $A$ to the midpoint of side $BC$ measures $5$ inches. Given that the area of triangle $ABC$ is $24$ square inches, find the length of side $BC$.

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