
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
A square sheet of paper has an area of $18 \text{ cm}^2$. The front is white and the back is black. The sheet is folded so that point $A$ on one side of the square rests on the line connecting the midpoint of an adjacent side to the opposite corner, dividing the square into visible areas of black and white. Determine the distance from $A$ to its original position if the visible black area equals the visible white area. Express your answer in simplest radical form.

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