
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 with Nozdryov. First, Nozdryov distributes 222 nuts into two boxes. After looking at the arrangement, Chichikov names any integer \( N \) from 1 to 222. After this, Nozdryov must move one or more nuts to an empty third box, if necessary, and then present Chichikov with one or two boxes that contain exactly \( N \) nuts in total. As a result, Chichikov will receive as many dead souls as the number of nuts Nozdryov moved. What is the maximum number of souls Chichikov can guarantee for himself, regardless of how Nozdryov plays?

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