
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
1. The point corresponding to the complex number $(2+i)i$ is in the second quadrant.
2. If $x+y<6$, then $x<3$ and $y<3$.
3. For a proposition and its converse, the negation and the contrapositive, the number of true propositions must be even.
4. The necessary and sufficient condition for the domain of $f(x) = \lg(x^2-bx+c)$ to be the set of real numbers is the same as the necessary and sufficient condition for the range to be the set of real numbers, both are $b^2-4c<0$; Among these, the correct propositions are numbered.

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