
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
The solutions to the equation \( x^3 - 4 \lfloor x \rfloor = 5 \), where \( x \) is a real number, are denoted by \( x_1, x_2, x_3, \ldots, x_k \) for some positive integer \( k \). Find \( \sum_{i=1}^{k} x_{i}^{3} \).

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