
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
Sergey wrote down numbers from 500 to 1499 in a row in some order. Under each number, except for the leftmost one, he wrote the greatest common divisor (GCD) of this number and its left neighbor, resulting in a second row of 999 numbers. Then, using the same rule, he obtained a third row of 998 numbers, from which he derived a fourth row of 997 numbers, and so on. He stopped when, for the first time, all the numbers in the current row turned out to be equal to one. What is the maximum number of rows he could have written by that moment?

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