
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
Person A and Person B are playing a game with the first 100 natural numbers. Person A will first write these 100 numbers in a certain sequence without Person B seeing it. Then, Person B can write down 50 numbers out of these 100 and ask Person A to arrange these 50 numbers in the order they appear in A's sequence. After seeing the results, Person B can ask for another set of 50 numbers and continue this process. What is the minimum number of times Person B needs to ask to ensure that they can determine the sequence written by Person A, regardless of the original sequence? Provide a proof for your conclusion.

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