
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 that the sum of the first $n$ terms of a sequence $\{a_{n}\}$ is $S_{n}$, $S_{n}=3a_{n}-3$. If there exist two terms $a_{m}$ and $a_{n}$ such that $a_{m} \cdot a_{n} = \frac{81}{16}$, then which of the following conclusions are correct? (Select all correct options)<br/>① The sequence $\{a_{n}\}$ is an arithmetic sequence;<br/>② The sequence $\{a_{n}\}$ is a geometric sequence;<br/>③ $m+n$ is a constant value;<br/>④ Let the sum of the first $n$ terms of a sequence $\{b_{n}\}$ be $T_{n}$, ${b_n}={\log_{\frac{3}{2}}}{a_n}$, then the sequence $\left\{{\frac{{{T_n}}}{n}}\right\}$ is an arithmetic sequence.

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