
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
Place 11 balls into three boxes such that the number of balls in each box is different. What is the maximum number of balls that can be placed in the fullest box, and what is the minimum number of balls that must be placed in the fullest box?

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