
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
A certain school has $5$ students preparing to participate in a charity event at a nursing home. Three students from Class A are represented by $A$, $B$, $C$, and two students from Class B are represented by $D$, $E$. Now, two students will be randomly selected from these $5$ students to take on the cleaning work at the nursing home.  
$(1)$ List all possible outcomes of the selection using the given letters.  
$(2)$ Let $M$ be the event "the 2 selected students are from the same class." Find the probability of event $M$ occurring.

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