
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, B, and C are three different workshops in a factory producing the same product, with the quantities (in units) shown in the table below. Quality inspectors use stratified sampling to select 6 samples from these products.

| Workshop | A   | B   | C   |
|----------|-----|-----|-----|
| Quantity | 10  | 20  | 30  |

$(1)$ Find the quantities of products from workshops A, B, and C in these 6 samples.  
$(2)$ If 2 samples are randomly selected from these 6 samples for testing, find the probability that both samples are from workshop C.

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