
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
Square $ABCD$ has side length $4$ units. Point $E$ is on side $AB$, and point $F$ is the reflection of $E$ over diagonal $AC$. If the distance from $D$ to $F$ is twice the length of $AE$, find the length of $AE$.

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