
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

Three pulleys with parallel axes and identical radii \( r = 2 \) cm need to be connected by a flat belt drive. The distance between the axes of rotation of pulleys \( O_{1} \) and \( O_{2} \) is 12 cm, and the distance between the axes of rotation of pulleys \( O_{1} \) and \( O_{3} \) is 10 cm. The distance from the axis \( O_{3} \) to the plane containing the axes \( O_{1} \) and \( O_{2} \) is 8 cm. Determine the length of the belt for the transmission, which is manufactured by sewing the ends of an inextensible rubberized cord (consider the length of the belt to be equal to the length of this cord). Is a 54 cm cord always sufficient for its manufacture?

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