
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 the following scenario, $ABCD$ is a square piece of paper with each side measuring 8 cm. Corner $C$ is folded over such that it coincides with $E$, located one-third of the way along $\overline{AD}$ from $A$ to $D$. If $\overline{GF}$ represents the crease created by the fold such that $F$ is on $\overline{CD}$, determine the length of $\overline{FD}$.

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