
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 four propositions:

1. If the area of $\triangle ABC$ is $\frac{\sqrt{3}}{2}$, $c=2$, $A=60^{\circ}$, then the value of $a$ is $\sqrt{3}$;  
2. In an arithmetic sequence $\{a_n\}$, $a_1=2$, $a_1$, $a_3$, $a_4$ form a geometric sequence, then the common difference is $-\frac{1}{2}$;  
3. In $\triangle ABC$, if $\sin^2A < \sin^2B+\sin^2C$, then $\triangle ABC$ is an acute triangle.  
The correct proposition number(s) is __________.

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