
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 three batches of parts, each containing 30 parts. The number of standard parts in the first, second, and third batches is 20, 15, and 10, respectively. A part is randomly selected from a randomly chosen batch and it turns out to be standard. Then, a second part is randomly selected from the same batch, and it also turns out to be standard. Find the probability that the parts were drawn from the third batch.

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