
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
Let  $a_1,a_2,\dots,a_{2021}$  be  $2021$  integers which satisfy
	\[ a_{n+5}+a_n>a_{n+2}+a_{n+3}\]
	for all integers  $n=1,2,\dots,2016$ . Find the minimum possible value of the difference between the maximum value and the minimum value among  $a_1,a_2,\dots,a_{2021}$ .

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