The function $f(x) = ax^2 + bx + c$ satisfies the following conditions:
1. $f(\sqrt{2}) = 3$
2. $|f(x)| \le 1$ for all $x \in [-1, 1]$.

Evaluate the value of $f(\sqrt{2013})$.

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