
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

Calibration of rollers. One of the components of a gasoline engine has the shape of a roller. A steel plate, which has 15 holes drilled in a row with precisely set dimensions, is used to measure the thickness of the roller. The first hole has a diameter of 10 mm, and each subsequent hole has a diameter that is 0.04 mm larger than the previous one. The calibration of the roller involves inserting it into a hole; if it does not fit, its diameter is considered to be larger than the hole's diameter, and if it fits, its diameter is considered to be smaller. Thus, eventually, the diameter of the roller is determined with an accuracy of less than 0.04 mm (rollers with a diameter less than 10 mm or greater than 10.56 mm are not considered; the others proceed to further processing).

Workers tasked with the calibration test each roller on the same number of holes, but, of course, on different holes. How many measurement attempts are necessary for each roller? What should be the sequence of attempts?

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