
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 $H$ be the midpoint of $CF$. Point $E$ is defined as the intersection of side $BC$ and line $BH$. Determine the ratio in which point $E$ divides side $BC$.
**A)** $\frac{4}{7}$
**B)** $\frac{7}{4}$
**C)** $\frac{3}{5}$
**D)** $\frac{5}{3}$
**E)** $\frac{6}{7}$

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