
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 certain factory is conducting random inspections on a batch of components. The probability of a component passing the first inspection is $0.8$. If a component fails the first inspection, it will be reworked and undergo a second inspection. The probability of a component passing the second inspection is $0.9$. If a component fails the second inspection as well, it will be scrapped. The probability of a component being scrapped is ______.

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