
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
Among the following propositions:
1. For the proposition p: $\exists x \in R$ such that $x^2 + x - 1 < 0$, the negation $\neg p$: $\forall x \in R$, $x^2 + x - 1 > 0$.
2. If p is a necessary but not sufficient condition for q, then $\neg p$ is a sufficient but not necessary condition for $\neg q$.
3. The proposition "If $\sin x \neq \sin y$, then $x \neq y$" is true.
4. $\lg x > \lg y$ is a necessary and sufficient condition for $x > y$.

The indices of all correct propositions are.

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