
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 two distinct points $M(x\_1,y\_1)$ and $N(x\_2,y\_2)$, and a line $l$: $ax+by+c=0$, with $δ= \frac {ax\_1+by\_1+c}{ax\_2+by\_2+c}$. The following propositions are given:

1. No matter the value of $δ$, point $N$ is not on line $l$;
2. If line $l$ is perpendicular to and bisects segment $MN$, then $δ=1$;
3. If $δ=-1$, then line $l$ passes through the midpoint of segment $MN$;
4. If $δ > 1$, then points $M$ and $N$ are on the same side of line $l$ and $l$ intersects the extension of segment $MN$.

Write down the sequence number(s) of all correct propositions.

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