
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
Ten people are sitting around a round table, each with a certain number of nuts. There are a total of one hundred nuts. At a common signal, each person passes some of their nuts to their right neighbor: half if they had an even number, or one nut plus half of the remainder if they had an odd number. This operation is performed.

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