
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
In the sequence $\{a_n\}$, $a_1 = \frac{1}{3}$, and the sum of the first $n$ terms $S_n$ satisfies $S_{n+1} - S_n = \left( \frac{1}{3} \right)^{n+1}$ ($n \in \mathbb{N}^*$).  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$ and the sum of the first $n$ terms $S_n$;  
(Ⅱ) If $S_1$, $t(S_1+S_2)$, $3(S_2+S_3)$ form an arithmetic sequence, find the value of the real number $t$.

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