
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
Inside a right triangle with sides 10, 24, and 26, three identical circles are inscribed such that each circle touches two sides of the triangle and two other circles. If each circle has a radius of 2, determine the total length of the segments from the vertices of the triangle to the points where the circles touch the sides.
A) 48
B) 50
C) 52
D) 54

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