
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
Let $[x]$ denote the greatest integer less than or equal to $x$. For example, $[3.15]=3,[3.7]=3,[3]=3$. Find the value of $[\sqrt[3]{1 \cdot 2 \cdot 3}]+[\sqrt[3]{2 \cdot 3 \cdot 4}]+[\sqrt[3]{3 \cdot 4 \cdot 5}]+\cdots+[\sqrt[3]{2000 \cdot 2001 \cdot 2002}]$.

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