
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
Given the following propositions:  
\\(①\\) The negation of the proposition "If \\(x^{2}=1\\), then \\(x=1\\)" is "If \\(x^{2}=1\\), then \\(x \neq 1\\)";  
\\(②\\) "\\(x=-1\\)" is a necessary but not sufficient condition for "\\(x^{2}-5x-6=0\\)";  
\\(③\\) The negation of the proposition "There exists \\(x \in \mathbb{R}\\) such that \\(x^{2}+x-1 < 0\\)" is: "For all \\(x \in \mathbb{R}\\), \\(x^{2}+x-1 > 0\\)";  
\\(④\\) The contrapositive of the proposition "If \\(x=y\\), then \\(\sin x = \sin y\\)" is true.  
Among these, the correct proposition numbers are __________.

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