
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
The positive integers \(1, 2, \cdots, n, \cdots\) are grouped such that the \(k\)th group contains \(k+1\) numbers:
\[
\begin{array}{l}
\underbrace{(1,2)}_{\text{1st group}}, \underbrace{(3,4,5)}_{\text{2nd group}}, \underbrace{(6,7,8,9)}_{\text{3rd group}}, \\
\underbrace{(10,11,12,13,14)}_{\text{4th group}}, \cdots
\end{array}
\]

Determine the group in which 2019 is located.

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