
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 $\triangle ABC$, point $F$ divides side $AC$ in the ratio $2:3$. Let $E$ be the point of intersection of side $BC$ and $AG$ where $G$ is the point on $BF$ such that $BG:GF = 3:2$. The point $E$ divides side $BC$ in what ratio?
**A)** 1:2
**B)** 2:1
**C)** 1:1
**D)** 2:3
**E)** 3:5

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