
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 the sets
$$
\begin{aligned}
A & = \{n(n+1) \mid n=1,2, \cdots\}, \\
B & = \{3m-1 \mid m=1,2, \cdots\}.
\end{aligned}
$$

If the elements of the set \( A \cap B \) are arranged in ascending order to form a sequence \(\{a_{k}\}\), find the general term formula \(a_{k} = \).

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