
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
Point $M$ is located on the plane of $\triangle ABC$ and satisfies $5 \overrightarrow{AM}= \overrightarrow{AB}+3 \overrightarrow{AC}$. Determine the ratio of the areas of $\triangle ABM$ and $\triangle ABC$.

A) $\frac{1}{5}$
B) $\frac{2}{5}$
C) $\frac{3}{5}$
D) $\frac{4}{5}$

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