
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
Given that a butterfly (whose volume is negligible) is freely flying inside a rectangular prism with lengths of 5, 4, and 3 respectively, if the butterfly always maintains a distance greater than 1 from the 6 faces of the rectangular prism, calculate the probability of the butterfly's "safe flight".

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