
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
When two fair dice are thrown once, let the number on the first die be $m$ and the number on the second die be $n$. For the vector $\overrightarrow{a}=(m-2,2-n)$ and the vector $\overrightarrow{b}=(1,1)$, determine the probability that the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to each other.

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