
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 pirate is now exploring 8 islands. On each island, there is a $\frac{1}{5}$ chance that the island has buried treasure and no traps, a $\frac{1}{10}$ chance that the island has traps but no treasure, and a $\frac{7}{10}$ chance that the island has neither traps nor treasure. What is the probability that while searching all 8 islands, the pirate will find exactly 4 islands with treasure and none with traps?

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