
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
Given a positive integer \( n \), Tom and Jerry are playing a game on a board with 2018 squares in a row. Initially, Jerry places a coin on one of the squares. In each subsequent step, Tom states a positive integer between \( 1 \) and \( n \) (inclusive). Jerry then decides whether to move the coin to the left or to the right by the number of squares selected by Tom. Tom wins if Jerry cannot move the coin. Find the smallest \( n \) such that Tom can ensure to win by choosing appropriate numbers in a finite number of moves.

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