
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\\) Given that \\(a\\) and \\(b\\) are real numbers, if \\(a+b\\) is a rational number, then \\(a\\) and \\(b\\) are both rational numbers;  
\\(②\\) If \\(a+b \geqslant 2\\), then at least one of \\(a\\) or \\(b\\) is not less than \\(1\\);  
\\(③\\) The solution to the inequality \\(ax+b > 0\\) with respect to \\(x\\) is \\(x > - \dfrac {b}{a}\\);  
\\(④\\) "The equation \\(ax^{2}+bx+c=0\\) has a root of \\(1\\)" is a necessary and sufficient condition for "\\(a+b+c=0\\)"  
Among these, the numbers of the true propositions are \_\_\_\_\_\_ \\((\\)please fill in the numbers of all true propositions\\()\\)

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