
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 located on side $BC$ such that $BD = 2DC$ and point $E$ is on side $AB$ such that $AE = 3EB$. If $F$ is the intersection point of $AD$ and $CE$, calculate the sum of the ratios $\frac{EF}{FC} + \frac{AF}{FD}$.

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