
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 the following propositions:  
① The area of a sector with a radius of 2 and a central angle of $\frac {1}{2}$ radians is $\frac {1}{2}$;  
② If $\alpha$ and $\beta$ are acute angles, and $\tan(\alpha +\beta )= \frac {1}{3}$, $\tan\beta = \frac {1}{2}$, then $\alpha +2\beta = \frac {\pi }{4}$;  
③ If A and B are two interior angles of $\triangle ABC$, and $\sin A < \sin B$, then $BC < AC$;  
④ If $a$, $b$, and $c$ are the lengths of the sides opposite to the angles A, B, and C in $\triangle ABC$, respectively, and $a^{2}+b^{2}-c^{2} < 0$, then $\triangle ABC$ is definitely an obtuse triangle.  
Among these propositions, the numbers of the true propositions are __________.

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