
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
Among the following propositions:<br/>① In $\triangle ABC$, if $\sin A \gt \sin B$, then $A \gt B$;<br/>② If $a \gt 0$, $b \gt 0$, and $a+b=4$, then the maximum value of $\sqrt{a+3}+\sqrt{b+2}$ is $3\sqrt{2}$;<br/>③ Given that the function $f\left(x\right)$ is a linear function, if the general term of the sequence $\{a_{n}\}$ is $a_{n}=f\left(n\right)$, then the sequence is an arithmetic sequence;<br/>④ If the general term of the sequence $\{b_{n}\}$ is $b_{n}=q^{n}$, then the sum of the first $n$ terms of the sequence $\{b_{n}\}$ is $S_{n}=\frac{{q(1-{q^n})}}{1-q}$.<br/>The correct proposition numbers are ____.

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