
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
There are the following propositions:  
\\(①\\) The negation of the proposition "There exists \\(x \in \mathbb{R}\\) such that \\(x^{2}+x+1=0\\)" is "There exists \\(x \in \mathbb{R}\\) such that \\(x^{2}+x+1 \neq 0\\)";  
\\(②\\) If \\(A=\{x|x > 0\}\\) and \\(B=\{x|x \leqslant -1\}\\), then \\(A \cap (\complement_{\mathbb{R}} B) = A\\);  
\\(③\\) The necessary and sufficient condition for the function \\(f(x)=\sin (\omega x+\phi) (\omega > 0)\\) to be an even function is \\(\phi=k\pi+ \frac {\pi}{2} (k \in \mathbb{Z})\\);  
\\(④\\) If non-zero vectors \\(\vec{a}, \vec{b}\\) satisfy \\(|\vec{a}|=|\vec{b}|=|\vec{a}- \vec{b}|\), then the angle between \\(\vec{b}\\) and \\(\vec{a}- \vec{b}\\) is \\(60^{\circ}\\).  
Among these, the correct propositions are \_\_\_\_\_\_ \\((\\)List all the numbers of propositions you think are true\\()\\).

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