
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
In a rectangular grid where grid lines are spaced $1$ unit apart, the acronym XYZ is depicted below. The X is formed by two diagonal lines crossing, the Y is represented with a 'V' shape starting from a bottom point going up to join two endpoints with horizontal lines, the Z is drawn with a top horizontal line, a diagonal from top right to bottom left and a bottom horizontal line. Calculate the sum of lengths of the line segments that form the acronym XYZ.
A) $6 + 3\sqrt{2}$
B) $4 + 5\sqrt{2}$
C) $3 + 6\sqrt{2}$
D) $5 + 4\sqrt{2}$

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