
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 pile of oranges is being sorted by a fruit sorting machine. It is known that the ratio of large oranges to small oranges in this pile is $3:2$. The probability that the sorting machine classifies a large orange as a small orange is $0.02$, and the probability that it classifies a small orange as a large orange is $0.05$. After one round of sorting, a "large orange" is randomly selected from the sorted ones. The probability that this "large orange" is indeed a large orange is ______.

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