
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 conclusions:

1. In $\triangle ABC$, if $A > B$, then $\sin A > \sin B$;
2. If $\overrightarrow{a} \cdot \overrightarrow{b} < 0$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is obtuse;
3. Translating the graph of the function $y=3\sin 2x$ to the right by $\frac{\pi}{3}$ units yields the graph of $f(x)=3\sin(2x-\frac{\pi}{3})$;
4. The range of the function $f(x)=2\sin(x+\frac{\pi}{6})\sin(\frac{\pi}{3}-x)$ on the interval $x\in[-\frac{\pi}{4},\frac{\pi}{4}]$ is $[- \frac{1}{2},1]$;
5. If $0 < \tan A \tan B < 1$, then $\triangle ABC$ is an obtuse triangle.

Determine the correct conclusion(s) by filling in the corresponding number(s).

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