
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
1. If the converse of a proposition is true, then its negation must also be true.
2. In $\triangle ABC$, "$\angle B=60^{\circ}$" is the necessary and sufficient condition for "$\angle A$, $\angle B$, $\angle C$ form an arithmetic sequence".
3. Given $a,b\in\mathbb{R}$, then "$ab=1$" is a sufficient but not necessary condition for the lines "$ax+y-1=0$" and "$x+by-1=0$" to be parallel.
4. "$am^2 < bm^2$" is the necessary and sufficient condition for "$a < b$".

Among the above statements, the correct ones are numbered \_\_\_\_\_\_.

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