
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
Determine the sum of the lengths of the line segments that form the acronym "BETA" shown on a rectangular grid with grid lines spaced 1 unit apart. The segments are as follows:
- 'B' includes two vertical segments of 2 units each, a horizontal segment on top and bottom (1 unit each), and a slanted segment forming a diagonal of a $1 \times 2$ rectangle.
- 'E' includes three horizontal segments of 1 unit each and one vertical segment of 2 units.
- 'T' includes one horizontal segment of 2 units and one vertical segment of 1 unit intersecting the middle of the horizontal segment.
- 'A' includes two slants forming diagonals of two $1 \times 1$ squares and a horizontal segment of 1 unit between the tops of the slants.
A) $14 + 2\sqrt{2} + \sqrt{5}$
B) $15 + 2\sqrt{2} + \sqrt{6}$
C) $15 + 3\sqrt{2}$
D) $13 + 2\sqrt{2} + \sqrt{5}$
E) $14 + \sqrt{2} + \sqrt{5}$

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