
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, the correct proposition number is ______.

(1) The negation of the proposition "If $x^{2}=1$, then $x=1$" is "If $x^{2}=1$, then $x\neq 1$";  
(2) The negation of the proposition "There exists an $x$ in $\mathbb{R}$ such that $x^{2}+x-1 < 0$" is "For all $x$ in $\mathbb{R}$, $x^{2}+x-1 > 0$";  
(3) The contrapositive of the proposition "If $x=y$, then $\sin x=\sin y$" is a false proposition;  
(4) If "Either $p$ or $q$ is a true proposition, then at least one of $p$, $q$ is a true proposition."

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