
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 *pucelana* sequence is an increasing sequence of  $16$  consecutive odd numbers whose sum is a perfect cube. How many pucelana sequences are there with  $3$ -digit numbers only?

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