Consider non-negative real numbers $a, b, c$ satisfying the condition $a^2 + b^2 + c^2 = 2$. Find the maximum value of the following expression:
\[
P = \frac{\sqrt{b^2 + c^2}}{3-a} + \frac{\sqrt{c^2 + a^2}}{3-b} + a + b - 2022c
\]

Let's think step by step and output the final answer within \boxed{}.
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