
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
Remove all perfect squares and perfect cubes from the set $A=\{n|n\leq10000, n\in\mathbb{N}^*\}$. Then, arrange the remaining elements in ascending order to form a sequence. The number 2014 is the $\boxed{\text{nth}}$ element of this sequence.

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