
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
A sequence $\{a\_n\}$ is defined by $a\_1= \frac {1}{3}$. The sum of the first $n$ terms, denoted by $S\_n$, satisfies the equation $S\_{n+1}-S\_n=(\frac {1}{3})^{n+1} (n \in \mathbb{N}^*)$.
(I) Find the general formula for the $n$-th term, $a\_n$, 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}
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