
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 equal radii \( r = 2 \) cm must be connected by a flat belt drive. The distance between the centers of rotation of pulleys \( O_1 \) and \( O_2 \) is 12 cm, and the distance between the centers of rotation of pulleys \( O_1 \) and \( O_3 \) is 10 cm. The distance from the axis \( O_3 \) to the plane in which the axes \( O_1 \) and \( O_2 \) lie is 8 cm. Determine the length of the belt required for this drive, which is made by sewing the ends of an inextensible rubberized cord together (assuming the belt length is equal to the length of this cord). Will a cord of 54 cm always be sufficient for its manufacture?

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