
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 a sequence $\{a_n\}$ that satisfies: $a_1 + 3a_2 + 5a_3 + \dots + (2n-1)a_n = (n-1)\cdot 3^{n+1} + 3$ ($n \in \mathbb{N}^*$), determine the general term formula $a_n$ for the sequence.

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