
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, when $P(x,y)$ is not the origin, define the "companion point" of $P$ as $P'( \dfrac {y}{x^{2}+y^{2}}, \dfrac {-x}{x^{2}+y^{2}})$. When $P$ is the origin, define its "companion point" as itself. Now, consider the following propositions:  
$\text{①}$ If the "companion point" of point $A$ is point $A'$, then the "companion point" of point $A'$ is point $A$.  
$\text{②}$ The "companion point" of a point on the unit circle is still on the unit circle.  
$\text{③}$ If two points are symmetric about the $x$-axis, then their "companion points" are symmetric about the $y$-axis.  
$\text{④}$ If three points lie on the same straight line, then their "companion points" must also be collinear.  
Among these propositions, the true ones are \_\_\_\_\_\_.

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