Let \( f: \mathbb{R} \to \mathbb{R} \) be a function such that 
\[ f(x + \lceil y \rceil) = f(x) + \lfloor y \rfloor \]
for all real numbers \( x \) and \( y \). If \( f(0) = 1 \), determine \( f(2.5) \). Let's think step by step and output the final answer within \boxed{}.
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