
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:
① In $\triangle ABC$, if $\sin A > \sin B$, then $A > B$;
② If $a > 0$, $b > 0$, and $a+b=4$, then the maximum value of $\sqrt{a+3} + \sqrt{b+2}$ is $3\sqrt{2}$;
③ Given that the function $f(x)$ is a linear function, if the general term of the sequence $\{a_n\}$ is $a_n=f(n)$, then the sequence is an arithmetic sequence;
④ 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 $S_n= \frac{q(1-q^n)}{1-q}$.
The correct proposition numbers are __________.

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