
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 D is the midpoint of side BC, and point E is one-third of the way from A to B (i.e., AE = 2EB). Point F is on side AD such that the segment AF is twice the length of segment FD. Calculate the sum of the ratios $\frac{EF}{FC} + \frac{AF}{FD}$.
A) $\frac{3}{2}$
B) $\frac{5}{2}$
C) 3
D) $\frac{7}{2}$

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