
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 treasure hunter is exploring 5 caves. In each cave, there is a $\frac{1}{5}$ chance that the cave has gold and no dangers, a $\frac{1}{10}$ chance that the cave has dangers but no gold, and a $\frac{4}{5}$ chance that the cave has neither gold nor dangers. What is the probability that while exploring all 5 caves, the treasure hunter will find exactly 2 caves with gold, and none with dangers?

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