
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
In the Cartesian coordinate system, let $M(x_{1}, y_{1})$ and $N(x_{2}, y_{2})$ be two different points, and the equation of line $l$ is $ax+by+c=0$. Let $δ=\frac{ax_{1}+by_{1}+c}{ax_{2}+by_{2}+c}$. The following three statements are given:<br/>① There exists a real number $\delta$ such that point $N$ lies on line $l$;<br/>② If $\delta = 1$, then the line passing through points $M$ and $N$ is parallel to line $l$;<br/>③ If $\delta = -1$, then line $l$ passes through the midpoint of line segment $MN$.<br/>The correct numbers of the above statements are ______.

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