
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
Four squares, each with a side length of 2 inches, are arranged horizontally. The second square from the left is rotated 45 degrees. Then it is centered and lowered into its original position until it touches both of the adjoining squares on either side. Determine the vertical distance from the highest point of the rotated square to the line on which the bases of the original squares rested.

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