
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
The squares of the first 2022 natural numbers are written in a row: \(1, 4, 9, \ldots, 4088484\). For each number written, except the first and the last, the arithmetic mean of its left and right neighbors is calculated and written below it (for example, below the number 4, \(\frac{1+9}{2}=5\) is written). The same procedure is repeated for the resulting sequence of 2020 numbers. This process continues until reaching a sequence with only two numbers. What are these two numbers?



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