
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
An acronym XYZ is drawn within a 2x4 rectangular grid with grid lines spaced 1 unit apart. The letter X is formed by two diagonals crossing in a $1 \times 1$ square. Y consists of a vertical line segment and two slanted segments each forming 45° with the vertical line, making up a symmetric letter. Z is formed by a horizontal segment at the top and bottom of a $1 \times 2$ rectangle, with a diagonal connecting these segments. In units, what is the total length of the line segments forming the acronym XYZ?
A) $5 + 4\sqrt{2} + \sqrt{5}$
B) $5 + 2\sqrt{2} + 3\sqrt{5}$
C) $6 + 3\sqrt{2} + 2\sqrt{5}$
D) $7 + 4\sqrt{2} + \sqrt{3}$
E) $4 + 5\sqrt{2} + \sqrt{5}$

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