
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
The following are four propositions:  
(1) $$\frac {1+i}{1-i}$$ is an element of the set M={m|m=i<sup>2</sup>, n∈N<sup>*</sup>} (where i is the imaginary unit);  
(2) p: The graph of the function f(x)=a<sup>x</sup>-2 (a>0, a≠1) always passes through the point (0, -2), q: The function f(x)=lg|x| (x≠0) has two zeros, then p∨q is a true proposition;  
(3) The maximum slope of the tangent line of the function f(x)=e<sup>-x</sup>-e<sup>x</sup> is 2;  
(4) ∃x<sub>0</sub>∈{x|x is irrational}, $$x_{0}^{2}$$ is irrational, among these propositions, the correct ones are ______.

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