
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 2-inch squares are aligned in a straight line. The second square from the left is rotated 90 degrees, and then shifted vertically downward until it touches the adjacent squares. Calculate the distance from point $C$, the top vertex of the rotated square, to the original line on which the bases of the squares were placed.

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