
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
Three workshops A, B, and C of a factory produced the same kind of product, with quantities of 120, 60, and 30, respectively. To determine if there are significant differences in product quality, a stratified sampling method was used to take a sample of size n for inspection, with 2 samples taken from workshop B.

(I) How many samples should be taken from workshops A and C, and what is the sample size n?
(II) Let the n samples be denoted by $A_1$, $A_2$, ..., $A_n$. Now, randomly select 2 samples from these.
(i) List all possible sampling outcomes.
(ii) Let M be the event "the 2 selected samples come from different workshops." Calculate the probability of event M occurring.

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