
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
Count a series of 7 Bernoulli trials, where a success is a hit that topples one of the two posts to which a red section of the fence is attached. The probability of success is $\frac{2}{7}$. Find the probability that the red section does not suffer (experiences 0 successes).

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