
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 eccentricity \\(e= \frac { \sqrt {5}}{3}\\) of the ellipse \\( \frac {x^{2}}{3}+ \frac {y^{2}}{2}=1\\), and its major axis is \\(2 \sqrt {3}\\);  
\\(②\\) The directrix equation of the parabola \\(x=2y^{2}\\) is \\(x=- \frac {1}{8}\\);  
\\(③\\) The asymptote equations of the hyperbola \\( \frac {y^{2}}{49}- \frac {x^{2}}{25}=-1\\) are \\(y=± \frac {5}{7}x\\);  
\\(④\\) The roots of the equation \\(2x^{2}-5x+2=0\\) can be used as the eccentricities of an ellipse and a hyperbola respectively.  
Among these, the correct propositions are \_\_\_\_\_\_.

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