
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
Given that
\[ x = \left\lfloor 1^{1/3} \right\rfloor + \left\lfloor 2^{1/3} \right\rfloor + \left\lfloor 3^{1/3} \right\rfloor + \cdots + \left\lfloor 7999^{1/3} \right\rfloor, \]
find the value of \(\left\lfloor \frac{x}{100} \right\rfloor\), where \(\lfloor y \rfloor\) denotes the greatest integer less than or equal to \( y \).

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