
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
There are 2016 cards, each with a unique number from 1 to 2016. A certain number \( k \) of these cards are selected. What is the smallest \( k \) such that among these selected cards, there exist two cards with numbers \( a \) and \( b \) satisfying the condition \( |\sqrt[3]{a} - \sqrt[3]{b}| < 1 \)?

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