
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 four one-inch squares are placed in a horizontal line, the third square from the left is lifted, rotated 45 degrees and repositioned in line such that its left diagonal point touches the right edge of the second square. Calculate the greatest vertical distance from the original line to any point on the repositioned rotated square.

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