
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
Among the following conclusions:  
\\(①\\) If \\(x > 0\\) and \\(y > 0\\), then " \\(x+2y=2 \sqrt {2xy}\\) " holds under a sufficient but not necessary condition that " \\(x=2\\) and \\(y=1\\) ";  
\\(②\\) There exists \\(a > 1\\) and \\(x > 0\\) such that \\(a^{x} < \log _{a}x\\);  
\\(③\\) If the derivative of the function \\(f(x)=x^{4}-(a-1)x^{2}+(a-3)x\\) is an odd function, then the real number \\(a=3\\);  
\\(④\\) The trajectory equation of a moving point \\(P\\) on a plane, which is at a distance greater than \\(1\\) from a fixed point \\(F(1,0)\\) compared to its distance from the \\(y\\)-axis, is \\(y^{2}=4x\\).  
The correct conclusion numbers are __________. (Fill in all the correct conclusion numbers)

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