
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 of numbers is *platense* if the first number is greater than  $1$ , and  $a_{n+1}=\frac{a_n}{p_n}$  which  $p_n$  is the least prime divisor of  $a_n$ , and the sequence ends if  $a_n=1$ . For instance, the sequences  $864, 432,216,108,54,27,9,3,1$  and  $2022,1011,337,1$  are both sequence platense. A sequence platense is *cuboso* if some term is a perfect cube greater than  $1$ . For instance, the sequence  $864$  is cuboso, because  $27=3^3$ , and the sequence  $2022$  is not cuboso, because there is no perfect cube. Determine the number of sequences cuboso which the initial term is less than  $2022$ .

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