
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
A geometric acronym XYZ is formed in a 4x12 unit grid where grid lines are spaced 1 unit apart. The letter X is formed with two diagonal segments connecting opposite corners of a 2x2 square, letter Y is formed using a vertical segment 2 units long with a 1 unit diagonal slant at the top, and Z is a combination of two horizontal 3-unit long segments at the top and bottom, connected by a 2 unit vertical segment in the middle right side. Calculate the total length of the line segments forming the XYZ in units.
A) $10 + 5\sqrt{2}$
B) $12 + 4\sqrt{2}$
C) $12 + 6\sqrt{2}$
D) $10 + 3\sqrt{2}$
E) $14 + 4\sqrt{2}$

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