
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
Two squirrels, Bushy and Jumpy, have collected  $2021$  walnuts for the winter. Jumpy numbers the walnuts from 1 through  $2021$ , and digs  $2021$  little holes in a circular pattern in the ground around their favourite tree. The next morning Jumpy notices that Bushy had placed one walnut into each hole, but had paid no attention to the numbering. Unhappy, Jumpy decides to reorder the walnuts, and Bushy decides to interfere with Jumpy. The two take turns to reorder the walnuts. Each time, Bushy chooses  $1232$  walnuts and reorders them and then Jumpy chooses  $n$  walnuts to reorder. Find the least positive integer  $n$  such that whatever Bushy does, Jumpy can ensure that the  $i$ th hole from the left has the  $i$ th walnut

*Ift0501*

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