
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 four propositions:

\\(①\\) The moving point \\(P\\) has a sum of distances to two fixed points \\({F}_1(-2,0), {F}_2(2,0)\\) equal to \\(4\\), then the trajectory of point \\(P\\) is an ellipse;

\\(②\\) Point \\(P\\) is on the parabola \\({y}^2=4x\\), \\(F\\) is the focus, and the fixed point \\(A(2,1)\\), then the minimum value of \\(|PF|+|PA|\\) is \\(3\\);

\\(③\\) The function \\(f(x)=x\cos x-\sin x\\) is monotonically increasing on \\((\pi,2\pi)\\);

\\(④\\) A differentiable function \\(f(x)\\) defined on \\(\mathbb{R}\\) satisfies \\(f''(1)=0\\) and \\((x-1)f'(x) > 0\\), then \\(f(0)+f(2) > 2f(1)\\) holds.

Among these, the serial numbers of all true propositions are $\boxed{\text{②③④}}$.

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