
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
A square sheet of paper that measures  $18$  cm on a side has corners labeled  $A$ ,  $B$ ,  $C$ , and  $D$  in clockwise order. Point  $B$  is folded over to a point  $E$  on  $\overline{AD}$  with  $DE=6$  cm and the paper is creased. When the paper is unfolded, the crease intersects side  $\overline{AB}$  at  $F$ . Find the number of centimeters in  $FB$ .

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