
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. When the sheet is folded such that point $A$ rests on the diagonal as shown in a previous setup, the visible black area equals the visible white area. Calculate the distance from $A$ to its original position. Express your answer in simplest radical form.

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