
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
Assume there are two boxes of components. The first box contains 10 pieces, including 3 defective ones; the second box contains 20 pieces, including 2 defective ones. Now, randomly choose one box and then randomly select 1 component from that box. Given that the selected component is defective, the probability that it was taken from the first box is ______.

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