
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 \((n+1)^{\alpha+1}-n^{\alpha+1} < n^{\alpha}(\alpha+1) < n^{\alpha+1}-(n-1)^{\alpha+1}, -1 < \alpha < 0\). Let \(x = \sum_{k=4}^{10^{6}} \frac{1}{\sqrt[3]{k}}\), find the integer part of \(x\).

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