
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 $AC$ are 5 inches and 8 inches, respectively. The median $AM$ from vertex $A$ to side $BC$ measures 5 inches. Additionally, the height from $A$ to side $BC$ is 4 inches. Determine the length of side $BC$.
A) 7 inches
B) $\sqrt{78}$ inches
C) 9 inches
D) 10 inches

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