
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

A and B play a game. Each has 10 tokens numbered from 1 to 10. The board consists of two rows of squares. The first row is numbered from 1 to 1492 and the second row from 1 to 1989. On the nth turn, A places his token number n on any empty square in either row, and B places his token on any empty square in the other row. B wins if the order of the tokens is the same in the two rows; otherwise, A wins. Which player has a winning strategy? 

Suppose each player has k tokens, numbered from 1 to k. Who has the winning strategy? Suppose that both rows are all the integers? Or both all the rationals?

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