
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
Let the six vertices of a regular hexagon with side length $1$ be $A_{1}$, $A_{2}$, $A_{3}$, $A_{4}$, $A_{5}$, $A_{6}$. Let $M=\{\overrightarrow{a}|\overrightarrow{a}=\overrightarrow{{A_i}{A_j}}(i,j=1,2,3,4,5,6,i\neq j)\}$. If we randomly select two elements $\overrightarrow{m}$ and $\overrightarrow{n}$ from $M$, then the probability that $\overrightarrow{m} \cdot \overrightarrow{n}=0$ is ____.

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