
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 researcher is studying 7 different ecosystems. In each ecosystem, there's a $\frac{1}{5}$ chance it has a stable population of a rare species (positive), a $\frac{1}{10}$ chance that it's disturbed by external factors (negative), and a $\frac{17}{20}$ chance it has neither (neutral). What is the probability that in examining all 7 ecosystems, exactly 4 will have a stable population without any external disturbance?

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