
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 edge lies on a diagonal of the square, splitting the visible areas into equal parts of black and white. Determine how far point $A$ is from its original position, expressed in simplest radical form.

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