
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
Given the general term formula of a sequence $a_n$ as follows:
$$
a_n = \begin{cases}
3n + 1, & \text{if } n \text{ is odd} \\
2n - 2, & \text{if } n \text{ is even}
\end{cases}
$$
calculate the value of $a_2a_3$.

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