
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 a circle: \\((x+\cos \theta)^{2}+(y-\sin \theta)^{2}=1\\), and a line \\(l\\): \\(y=kx\\). Consider the following four propositions:  
\\(①\\) For any real numbers \\(k\\) and \\(\theta\\), the line \\(l\\) and the circle \\(M\\) have common points;  
\\(②\\) For any real number \\(k\\), there exists a real number \\(\theta\\) such that the line \\(l\\) is tangent to the circle \\(M\\);  
\\(③\\) For any real number \\(\theta\\), there exists a real number \\(k\\) such that the line \\(l\\) is tangent to the circle \\(M\\);  
\\(④\\) There exist real numbers \\(k\\) and \\(\theta\\) such that a point on the circle \\(M\\) is at a distance of \\(3\\) from the line \\(l\\).  
Among these propositions, the correct ones are \_\_\_\_\_\_ \\((\\)list all correct proposition numbers\\()\\)

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