
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 rectangle $ABCD$, $AB = 6$ and $BC = 8$. The rectangle is folded such that point $A$ is brought directly to point $D$, forming a new pentagonal shape $ABEFD$. Determine the length of segment $EF$. Express your answer in simplest radical form.

[asy]
size(200);
defaultpen(linewidth(.8pt)+fontsize(10pt));
draw((0,0)--(8,0)--(8,6)--(0,6)--(0,0)--cycle);
draw((14,6)--(21,0), dashed);
draw((21,6)--(14,6)--(11,0)--(11+2.4,-1.8)--(21,0)--(21,6)--cycle);
draw((14,6)--(21,0));

label("A", (0,6), NW);
label("B", (0,0), SW);
label("C", (8,0), SE);
label("D", (8,6), NE);
label("B", (19.2,-1.8), SE);
label("D", (21,6), NE);
label("E", (11,0), SW);
label("F", (14,6), N);
label("A$\&$D", (21,0), SE);
[/asy]

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