
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 pile of apples, the ratio of large apples to small apples is $9:1$. Now, a fruit sorting machine is used for screening, with a probability of $5\%$ that a large apple is sorted as a small apple and a probability of $2\%$ that a small apple is sorted as a large apple. Calculate the probability that a "large apple" selected from the sorted apples is indeed a large apple.

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