
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 $α$ and $β$ belong to the interval $\left[-\dfrac{π}{2}, \dfrac{π}{2}\right]$ and it holds that $α\sin α - β\sin β > 0$, identify the correct statement(s) among the following: 
1. $α > β$; 
2. $α < β$; 
3. $α + β > 0$; 
4. $α^{2} > β^{2}$; 
5. $α^{2} \leqslant β^{2}$.

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