
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 curve \\(C\\): \\( \dfrac{x|x|}{{a}^{2}}+ \dfrac{y|y|}{{b}^{2}}=1 \\), consider the following statements:

\\(①\\) A line perpendicular to the \\(x\\)-axis intersects the curve \\(C\\) at only one point.

\\(②\\) A line \\(y=kx+m\\) (where \\(k,m∈R\\)) intersects the curve \\(C\\) at most at three points.

\\(③\\) The curve \\(C\\) is symmetric about the line \\(y=x\\).

\\(④\\) If \\({P}_{1}({x}_{1},{y}_{2}), {P}_{2}({x}_{2},{y}_{2}) \\) are any two points on the curve \\(C\\), then \\( \dfrac{{y}_{1}-{y}_{2}}{{x}_{1}-{x}_{2}} < 0 \\).

Write down the correct statement numbers \_\_\_\_\_\_ .

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