
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
We say an integer  $n$  is naoish if  $n \geq 90$  and the second-to-last digit of  $n$  (in decimal notation) is equal to  $9$ . For example,  $10798$ ,  $1999$  and  $90$  are naoish, whereas  $9900$ ,  $2009$  and  $9$  are not. Nino expresses 2020 as a sum:
    \[
    2020=n_{1}+n_{2}+\ldots+n_{k}
    \]
    where each of the  $n_{j}$  is naoish.

    What is the smallest positive number  $k$  for which Nino can do this?

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