
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
There are  $2018$  players sitting around a round table. At the beginning of the game we arbitrarily deal all the cards from a deck of  $K$  cards to the players (some players may receive no cards). In each turn we choose a player who draws one card from each of the two neighbors. It is only allowed to choose a player whose each neighbor holds a nonzero number of cards. The game terminates when there is no such player. Determine the largest possible value of  $K$  such that, no matter how we deal the cards and how we choose the players, the game always terminates after a finite number of turns.

*Proposed by Peter Novotný, Slovakia*

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