
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 set \( A = \{ n(n+1) \mid n=1,2, \cdots \} \) and the set \( B = \{ 3m-1 \mid m=1,2, \cdots \} \). If the elements of the set \( A \cap B \) are arranged in ascending order to form a sequence \(\{ a_k \}\), then the general term of the sequence \(\{ a_k \}\) is \( a_k = \) _______.

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