
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
Three parallel lines  $L_1, L_2, L_2$  are drawn in the plane such that the perpendicular distance between  $L_1$  and  $L_2$  is  $3$  and the perpendicular distance between lines  $L_2$  and  $L_3$  is also  $3$ . A square  $ABCD$  is constructed such that  $A$  lies on  $L_1$ ,  $B$  lies on  $L_3$  and  $C$  lies on  $L_2$ . Find the area of the square.

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