
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 natural number is called a square if it can be written as the product of two identical numbers. For example, 9 is a square because \(9 = 3 \times 3\). The first squares are 1, 4, 9, 16, 25, ... A natural number is called a cube if it can be written as the product of three identical numbers. For example, 8 is a cube because \(8 = 2 \times 2 \times 2\). The first cubes are 1, 8, 27, 64, 125, ...

On a certain day, the square and cube numbers decided to go on strike. This caused the remaining natural numbers to take on new positions:

a) What is the number in the 12th position?

b) What numbers less than or equal to 2013 are both squares and cubes?

c) What is the new position occupied by the number 2013?

d) Find the number that is in the 2013th position.

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