
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
In a batch of 100 components, there are 20 first-class items, 30 second-class items, and 50 third-class items. A sample of 20 items is drawn from the batch using three different methods:

1) Simple random sampling: The components are numbered from 00 to 99, and 20 are drawn;

2) Systematic sampling: The components are divided into 20 groups of 5 each, and then 1 is randomly drawn from each group;

3) Stratified sampling: 4 items are randomly drawn from the first-class items, 6 from the second-class items, and 10 from the third-class items.

What is the probability that each item is drawn?

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