
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
Polikarp has 2 boxes: the first box contains $n$ coins, while the second one is empty. In one move, he can either transfer one coin from the first box to the second box or remove exactly $k$ coins from the first box, where $k$ is the number of coins in the second box. For which values of $n$ can Polikarp make the first box empty in no more than 10 moves?

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