
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 XYZ is arranged on a rectangular grid where grid lines are spaced $1$ unit apart. The letter X is formed by two diagonal segments from top left to bottom right and top right to bottom left of a square. Y is made of a vertical line from top to bottom mid-point and two diagonal segments connecting this point to the bottom corners. Z is made of one horizontal segment at the top, one diagonal segment from top right to bottom left, and one horizontal segment at the bottom. Calculate the sum of lengths of the line segments forming XYZ.
A) $3 + 4\sqrt{2}$
B) $3 + 5\sqrt{2}$
C) $5 + 3\sqrt{2}$
D) $4 + 5\sqrt{2}$
E) $5 + 5\sqrt{2}$

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