
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 sum of the first $n$ terms of a geometric sequence $\{a_n\}$ is $S_n$. Given $a_1=1$ and $\frac{S_{10}}{S_{5}}= \frac{33}{32}$.

(Ⅰ) Find the general formula for $\{a_n\}$.

(Ⅱ) Let $b_n= \frac{3n-1}{a_n}$. Find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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