
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
Let  $ABCD$  be a square, and let  $l$  be a line passing through the midpoint of segment  $AB$  that intersects segment  $BC$ . Given that the distances from  $A$  and  $C$  to  $l$  are  $4$  and  $7$ , respectively, compute the area of  $ABCD$ .

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