
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
A random variable $\xi$ follows a negative binomial distribution $\mathrm{P}(\xi=k)=C_{m+k-1}^{k} p^{m} q^{k}$. Here, $m>1$ and $p \in(0,1)$ are parameters, with $q=1-p$. Given a sample $x_{1}, \ldots, x_{n}$ of values of $\xi$, empirical moments $M_{1}=\bar{x}=1.21$ and $M_{2}=\overline{x^{2}}=3.54$ are determined. Using these moments, find the parameters $m$ and $p$.

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