
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 placed along a straight line. The second square from the left is lifted out and rotated by 30 degrees. Then it is repositioned centered horizontally between the first and third squares and lowered back until it touches the two adjacent squares. Calculate the vertical distance from the highest point of the rotated square to the line on which the bases of the other squares are placed.

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