
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 reconnaissance squad has 12 soldiers, including 3 radio operators. These 12 soldiers are to be randomly divided into 3 groups, with 3 soldiers, 4 soldiers, and 5 soldiers in each group. What is the probability that each group includes exactly 1 radio operator?

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