
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 $\{a_n\}$ satisfying $a_n = 3a_{n-1} + 3^{n-1}$ (where $n \in \mathbb{N^*}, n \geq 2$) and $a_1 = 5$. If $b_n = \frac{1}{3^n}(a_n+t)$ (where $n \in \mathbb{N^*}$) and $\{b_n\}$ is an arithmetic sequence, then $t = \_\_\_\_\_\_$.

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