
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
(i) Expand and simplify \((x+1)(x^{2}-x+1)\).

(ii) Find all powers of 2 that are one more than a cube. (A power of 2 is a number that can be written in the form \(2^{n}\), where \(n\) is an integer greater than or equal to 0.)

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