
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
The following diagram shows a square where each side has seven dots that divide the side into six equal segments. All the line segments that connect these dots that form a  $45^{\circ}$  angle with a side of the square are drawn as shown. The area of the shaded region is 75. Find the area of the original square.

[center]![Image](https://i.snag.gy/Jzx9Fn.jpg)[/center]

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