
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 a modified sequence of integers $\{b_1, b_2, b_3, \ldots \} = \{2, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, \ldots \}$, where each even positive integer $2k$ appears $k^2$ times. This sequence is generated by a formula $b_n = k\lfloor \sqrt{n+m} \rfloor + l$, where $k$, $m$, and $l$ are integers. If $b_1 = 2$, determine the sum $k+m+l$. The sequence ensures all numbers are even.
A) 1
B) 2
C) 3
D) 4
E) 5

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