
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 $a_n=3a_{n-1}+3^n-1$ ($n\in\mathbb{N}^*$, $n\geq2$),  
Given $a_3=95$.  
(1) Find $a_1$, $a_2$;  
(2) Is there a real number $t$ such that $$b_{n}= \frac {1}{3^{n}}(a_{n}+t) \quad (n\in\mathbb{N}^{*})$$, and $\{b_n\}$ is an arithmetic sequence? If it exists, find the value of $t$; if not, explain why.

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