
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
Consider the sequence of non-decreasing integers:
\[1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,\ldots\]
in which each integer $n$ appears $n$ times. Find the remainder when the $2000^{th}$ term is divided by $6$.
- A) 0
- B) 1
- C) 2
- D) 3
- E) 4
- F) 5

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