
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 the line $l: x+2y+1=0$, and the set $A=\{n|n<6, n\in \mathbb{N}^*\}$, if we randomly select 3 different elements from set $A$ to be $a$, $b$, and $r$ in the circle equation $(x-a)^2+(y-b)^2=r^2$, then the probability that the line connecting the center $(a, b)$ of the circle to the origin is perpendicular to line $l$ equals \_\_\_\_\_\_.

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