
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
Consider a square piece of paper $ABCD$ with each side measuring 8 cm. Corner $C$ is precisely folded such that it coincides with point $E$ located one-third the distance from $A$ to $D$ along $\overline{AD}$. When folded, $\overline{GF}$ represents the crease, with point $F$ falling on $\overline{CD}$. Determine the length of $\overline{FD}$, expressing your answer as a common fraction.

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