
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
Given three rectangles each measuring 2 inches by 1 inch placed along a horizontal line, one of the middle rectangle is lifted out, rotated 90 degrees, centered, and placed back, calculate the distance from the top vertex of the rotated rectangle to the line on which the bases of the original rectangles were placed.

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