
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 plane vectors $\overrightarrow{a_m} = (m, 1)$ and $\overrightarrow{b_n} = (2, n)$, where $m, n \in \{1, 2, 3\}$. Denote the event "making $\overrightarrow{a_m} \perp (\overrightarrow{a_m} - \overrightarrow{b_n})$ hold" as event A. Find the probability of event A occurring.

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