
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
On the median $BD$ of triangle $ABC$, whose area is $S$, a point $E$ is taken such that $DE=\frac{1}{4} BD$. A line $AE$ is drawn through point $E$, intersecting side $BC$ at point $F$. Find the area of triangle $AFC$.

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