
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
Find all the real numbers \(x\) such that:
$$
\left\{(x+1)^{3}\right\} = x^{3}
$$
where \(\{x\}\) denotes the fractional part of \(x\).

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