
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 searching for buried treasure on 7 islands. Each island has a $\frac{1}{5}$ chance of containing buried treasure and no traps, a $\frac{1}{10}$ chance of having traps but no treasure, and a $\frac{7}{10}$ chance of having neither traps nor treasure. What is the probability that, after exploring all 7 islands, the pirate finds exactly 4 islands with treasure and none with traps?

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