
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 functions \\(y=|x|\\) and \\(y=(\sqrt{x})^2\\) represent the same function;
\\(②\\) The graph of an odd function always passes through the origin of the coordinate system;
\\(③\\) The graph of the function \\(y=3(x-1)^2\\) can be obtained by shifting the graph of \\(y=3x^2\\) one unit to the right;
\\(④\\) The minimum value of \\(y=2^{|x|}\\) is \\(1\\);
\\(⑤\\) If for the function \\(f(x)\\), \\(f(-1) \cdot f(3) < 0\\), then the equation \\(f(x)=0\\) has a real root in the interval \\([-1,3]\\).

Identify the sequence numbers of the correct propositions. \_\_\_\_\_\_ \(.\) (Fill in the sequence numbers of all correct propositions\()\)

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