
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 the positive integer \( n \), if the expansion of \( (xy - 5x + 3y - 15)^n \) is combined and simplified, and \( x^i y^j \) (where \( i, j = 0, 1, \ldots, n \)) has at least 2021 terms, what is the minimum value of \( n \)?

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