
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 20 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 one of these batches and is found to be standard. After returning the part to the batch, another part is randomly selected from the same batch and is also found to be standard. Find the probability that the parts were selected from the third batch.

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