
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
Chichikov is playing a game with Nozdryov. Initially, Nozdryov distributes 222 nuts into two boxes. After observing the distribution, Chichikov announces any integer \( N \) from 1 to 222. Then, Nozdryov can move one or more nuts to an empty third box if necessary, and he must present Chichikov with one or two boxes containing exactly \( N \) nuts in total. As a result, Chichikov will gain as many dead souls as the number of nuts Nozdryov moved. What is the maximum number of souls Chichikov can guarantee himself, regardless of how Nozdryov plays?

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