
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
Suppose $(p_i),$ $(q_i),$ $(r_i)$ represent the entries in rows $2021$, $2022$, $2023$ of Pascal's triangle, respectively. Additionally, consider polynomials $P(x) = \sum_{i = 0}^{2021} {p_i \cdot x^i}$ and $Q(x) = \sum_{i = 0}^{2022} {q_i \cdot x^i}$. Calculate the degree and the leading coefficient of the polynomial given by $P(x) \cdot Q(x)$.

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