
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
For his birthday, Piglet baked a big cake weighing 10 kg and invited 100 guests. Among them was Winnie-the-Pooh, who has a weakness for sweets. The birthday celebrant announced the cake-cutting rule: the first guest cuts themselves a piece of cake equal to \(1\%\) of the remaining cake, the second guest cuts themselves a piece of cake equal to \(2\%\) of the remaining cake, the third guest cuts themselves a piece of cake equal to \(3\%\) of the remaining cake, and so on. Which position in the queue should Winnie-the-Pooh take to get the largest piece of cake?

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