
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 $\{a\_n\}$, the sum of its first $n$ terms is denoted as $S\_n$. The sequence is defined as $a\_1=t$, $a\_{n+1}=2S\_n+1$, where $n∈N^{*}$.

(I) For what value of the real number $t$ is the sequence $\{a\_n\}$ a geometric sequence?

(II) Under the conclusion of (I), let $b\_n=\\log \_{3}a\_{n+1}$. $T\_n$ is the sum of the first $n$ terms of the sequence $\{ \frac {1}{b\_n \cdot b\_{n+1}}\}$. Find the value of $T\_{2011}$.

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