
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 are four propositions:

1. The line $(3+m)x+4y-3+3m=0 (m∈R)$ always passes through the fixed point $(-3,3)$;
2. The endpoint $B$ of line segment $AB$ has coordinates $(3,4)$, and $A$ moves on the circle $x^{2}+y^{2}=4$, then the trajectory equation of the midpoint $M$ is $(x- \frac {3}{2})^{2}+(y-2)^{2}=1$;
3. Given $M={(x,y)|y= \sqrt {1-x^{2}}}$, $N={(x,y)|y=x+b}$, if $M∩N≠ ∅$, then $b∈[- \sqrt {2}, \sqrt {2}]$;
4. Given circle $C$: $(x-b)^{2}+(y-c)^{2}=a^{2}(a > 0,b > 0,c > 0)$, it intersects with the $x$-axis and is separated from the $y$-axis, then the intersection point of the line $ax+by+c=0$ and the line $x+y+1=0$ is in the second quadrant.

Among them, the correct propositions are ________ (fill in the blanks with the serial numbers of all correct conclusions)

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