
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
In $\triangle ABC$, the sides opposite $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$, respectively. Consider the following propositions: ① In $\triangle ABC$, $A > B$ is a sufficient but not necessary condition for $\sin A > \sin B$; ② In $\triangle ABC$, $A > B$ is a necessary and sufficient condition for $\cos A < \cos B$; ③ In $\triangle ABC$, $A > B$ is a necessary but not sufficient condition for $\tan A > \tan B$. Among these, the correct proposition(s) is/are numbered as ______.

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