
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
Players A and B play a game. They are given a box with  $n=>1$  candies. A starts first. On a move, if in the box there are  $k$  candies, the player chooses positive integer  $l$  so that  $l<=k$  and  $(l, k) =1$ , and eats  $l$  candies from the box. The player who eats the last candy wins. Who has winning strategy, in terms of  $n$ .

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