
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
There is a public phone booth with a phone inside. When observing the flow of people using this phone, let the probability that there are _\\(n\\)_ people using or waiting to use the phone at a certain moment be \\(P(\\)_\\(n\\)_\\()\\), and \\(P(\\)_\\(n\\)_\\()\\) is independent of the moment _\\(t\\)_. It is statistically found that \\(P\\left(n\\right)=\\begin{cases}\\left( \\dfrac{1}{2}\\right)^n\\cdot P\\left(0\\right), & 1\\leqslant n\\leqslant 6 \\\\ 0, & n\\geqslant 7\\end{cases} \\). Then, at a certain moment, the probability that there is no one in this public phone booth \\(P(0)\\) is \_\_\_\_\_\_.

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