
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
Petya and Vasya came up with ten fifth-degree polynomials. Then Vasya sequentially called out consecutive natural numbers (starting from a certain number), and Petya substituted each called number into one of the polynomials of his choice and wrote the resulting values in order from left to right on the board. It turned out that the numbers written on the board formed an arithmetic progression (in this order). What is the maximum number of numbers Vasya could have called out?

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