
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
Andrew takes a square sheet of paper  $ABCD$  of side length  $1$  and folds a kite shape. To do this, he takes the corners at  $B$  and  $D$  and folds the paper such that both corners now rest at a point  $E$  on  $AC$ . This fold results in two creases  $CF$  and  $CG$ , respectively, where  $F$  lies on  $AB$  and  $G$  lies on  $AD$ . Compute the length of  $FG$ .

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