
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
The acronym SUV is shown in the rectangular grid below with grid lines spaced 1 unit apart. In units, what is the sum of the lengths of the line segments that form the acronym SUV?
Consider the following updates in the grid drawing:
- "S" is represented with a curve resembling the shape 5 on a digital clock, using 9 total segments including slanted lines.
- "U" is placed using a vertical and a rounded bottom that looks like an upside-down "n" using 6 total line segments.
- "V" is depicted in typical V-shape using just the two slanted lines.
Assume all slanted segments are diagonals of 1x1 squares in the grid.
A) 11 + 4√2
B) 11
C) 11 + 6√2
D) 9 + 6√2
E) 17 + 6√2

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