
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
Arrange positive integers that are neither perfect squares nor perfect cubes (excluding 0) in ascending order as 2, 3, 5, 6, 7, 10, ..., and determine the 1000th number in this sequence.

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