
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 is a two-player game with 13 Go stones (13 is used for the game). The order of play is determined by drawing lots, and the player who goes first is called the "first player," while the other is called the "second player." The game rules are as follows: The first player must choose to take either 1 or 2 stones; after the first player takes their turn, the second player then starts their turn, following the same rules. Both players take turns until all the stones are taken. The player who takes the last stone wins. The first player has a winning strategy. If they want to win, the number of stones left for the opponent should be $\qquad$ from the first round until the end.

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