
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 on line segment $BC$ such that $BD:DC = 2:1$ and point $E$ is on line segment $AC$, dividing it as $AE:EC = 1:2$. Compute the sum of the ratios $\frac{EF}{FC} + \frac{AF}{FD}$.
A) $\frac{7}{3}$
B) $\frac{9}{3}$
C) $\frac{10}{3}$
D) $4$

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