
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
There are  $15$  people, including Petruk, Gareng, and Bagong, which will be partitioned into  $6$  groups, randomly, that consists of  $3, 3, 3, 2, 2$ , and  $2$  people (orders are ignored). Determine the probability that Petruk, Gareng, and Bagong are in a group.

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