
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 $\triangle ABC$, $D$ and $E$ are the midpoints of $BC$ and $AC$ respectively, and $F$ is a point on $AB$ such that $\overrightarrow{AB} = 4\overrightarrow{AF}$. If $\overrightarrow{AD} = x\overrightarrow{AF} + y\overrightarrow{AE}$, then $x+y= \_\_\_\_\_$.

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