
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
Find the number of sequences with  $2022$  natural numbers  $n_1, n_2, n_3, \ldots, n_{2022}$ , such that in every sequence: $\bullet$   $n_{i+1}\geq n_i$  $\bullet$  There is at least one number  $i$ , such that  $n_i=2022$  $\bullet$  For every  $(i, j)$   $n_1+n_2+\ldots+n_{2022}-n_i-n_j$  is divisible to both  $n_i$  and  $n_j$ 

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