
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 propositions, the correct ones are numbered \_\_\_\_\_\_.
\\(①\\) If the equation \\(a^{2}x^{2}+(a+2)y^{2}+2ax+a=0\\) represents a circle, then the real number \\(a=-1\\);
\\(②\\) Given that the graph of the function \\(f(x)=(\frac{1}{2})^{x}\\) is symmetric to the graph of the function \\(y=g(x)\\) about the line \\(y=x\\), let \\(h(x)=g(1-x^{2})\\), then the graph of \\(h(x)\\) is symmetric about the origin;
\\(③\\) In the cube \\(ABCD-A_{1}B_{1}C_{1}D_{1}\\), where \\(E\\) and \\(F\\) are the midpoints of \\(AB\\) and \\(AA_{1}\\) respectively, then the lines \\(CE\\), \\(D_{1}F\\), and \\(DA\\) intersect at a single point;
\\(④\\) The graph of a power function cannot pass through the fourth quadrant.

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