
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
Let \(\xi_{1}, \ldots, \xi_{n}\) be independent Bernoulli random variables,

$$
\mathbf{P}\left\{\xi_{k}=1\right\}=p, \quad \mathbf{P}\left\{\xi_{k}=0\right\}=1-p, \quad 1 \leqslant k \leqslant n
$$

Find the conditional probability that the first success (\(1\)) appears on the \(m\)-th step, given that a success occurred only once in all \(n\) steps.

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