
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 terms of the sequence $\{a_{n}\}$ are all positive numbers, and the sum of the first $n$ terms $S_{n}$ satisfies $a_{n}\cdot S_{n}=9$ for all $n=1,2,\ldots$. Four conclusions are given below:<br/>① The second term of $\{a_{n}\}$ is less than $3$;<br/>② $\{a_{n}\}$ is a geometric sequence;<br/>③ $\{a_{n}\}$ is a decreasing sequence;<br/>④ There exists a term in $\{a_{n}\}$ that is less than $\frac{1}{{100}}$.<br/>The correct conclusions are represented by the numbers ____.

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