
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 rectangular sheet of paper has dimensions $3 \text{ cm}$ by $4 \text{ cm}$. The front is white and the back is black. When the sheet is folded so that point $A$ on the shorter side rests on the longer side, making sure the fold is perpendicular to the longer side, the visible black area is equal to the visible white area. Calculate how many centimeters point $A$ is from its original position. Express your answer in simplest radical form.

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