
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
The sequence $\{a\_n\}$ satisfies the condition: $a\_1 + 3a\_2 + 5a\_3 + ... + (2n - 1) \cdot a\_n = (n - 1) \cdot 3^{n+1} + 3 \quad (n \in \mathbb{N}^*)$. Determine the general term formula for this sequence, $a\_n =$ \_\_\_\_\_\_\_.

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