
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
A sequence  $\{a_n\}$  is defined such that  $a_i=i$  for  $i=1,2,3\ldots,2020$  and for  $i>2020$ ,  $a_i$  is the average of the previous  $2020$  terms. What is the largest integer less than or equal to  $\displaystyle\lim_{n\to\infty}a_n$ ?

*2020 CCA Math Bonanza Lightning Round #4.4*

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