
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 $ABC$, where $AB = 6$ and $AC = 10$. Let $M$ be a point on $BC$ such that $BM : MC = 2:3$. If $AM = 5$, what is the length of $BC$?
A) $7\sqrt{2.2}$
B) $5\sqrt{6.1}$
C) $10\sqrt{3.05}$
D) $15 - 3\sqrt{6.1}$

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