
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
Initially, a natural number  $n$  is written on the blackboard. Then, at each minute, *Neymar* chooses a divisor  $d>1$  of  $n$ , erases  $n$ , and writes  $n+d$ . If the initial number on the board is  $2022$ , what is the largest composite number that *Neymar* will never be able to write on the blackboard?

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