
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
In the Rutherford and Geiger observations, a radioactive substance emitted an average of $3.87 \alpha$-particles over a period of 7.5 seconds. Find the probability that this substance will emit no $\alpha$-particles in one second.

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