
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  $n$  cards. Max and Lewis play, alternately, the following game
Max starts the game, he removes exactly  $1$  card, in each round the current player can remove any quantity of cards, from  $1$  card to  $t+1$  cards, which  $t$  is the number of removed cards by the previous player, and the winner is the player who remove the last card. Determine all the possible values of  $n$  such that Max has the winning strategy.

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