
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
When the Absent-Minded Scientist comes up with a genius idea, he writes it down on a piece of paper but immediately realizes that the idea is not genius, crumples the paper and throws it under the table where there are two trash bins. The scientist misses the first bin with probability \( p > 0.5 \), and he misses the second bin with the same probability. Over the course of a morning, the scientist throws five crumpled genius ideas under the table. Find the probability that each bin contains at least one of the morning's ideas.

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