
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
Determine the smallest integer  $n \ge 4$  for which one can choose four different numbers  $a, b, c, $  and  $d$  from any  $n$  distinct integers such that  $a+b-c-d$  is divisible by  $20$  .

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