
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, define $d(P, Q) = |x_1 - x_2| + |y_1 - y_2|$ as the "polyline distance" between two points $P(x_1, y_1)$ and $Q(x_2, y_2)$. Under this definition, consider the following propositions:  
① The set of points whose "polyline distance" from the origin is equal to 1 forms a square;  
② The set of points whose "polyline distance" from the origin is equal to 1 forms a circle;  
③ The set of points whose sum of "polyline distances" to points $M(-1, 0)$ and $N(1, 0)$ is 4 forms a hexagon with an area of 6;  
④ The set of points whose absolute difference in "polyline distances" to points $M(-1, 0)$ and $N(1, 0)$ is 1 forms two parallel lines.  
Among these propositions, the correct ones are. (Write down the numbers of all correct propositions)

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