
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 the angles $\angle A$, $\angle B$, $\angle C$ to form an arithmetic sequence.
3. The condition $\begin{cases} x > 1 \\ y > 2 \end{cases}$ is the necessary and sufficient condition for $\begin{cases} x+y > 3 \\ xy > 2 \end{cases}$.
4. "$am^{2} < bm^{2}$" is the necessary and sufficient condition for "$a < b$".
Among the above statements, the correct judgments are \_\_\_\_\_\_.

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