
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
$ABCD$ is a rectangular sheet of paper that has been folded so that corner $A$ is matched with point $A'$ on edge $BC.$ The crease is $GH,$ where $G$ is on $AB$ and $H$ is on $CD.$ The dimensions $BG=12, AG=5,$ and $DH=7$ are given. The area of rectangle $ABCD$ is to be calculated.

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