Please reason step by step, and put your final answer within \boxed{}.
Given a function \( f(x) \) defined on \( \mathbb{R} \) such that for any \( x \in \mathbb{R} \), the following conditions hold:
$$
\begin{array}{l}
f(-x)+f(x)=0 \\
f(x+1)+f(x)=0
\end{array}
$$

Additionally, when \( x \in (0,1) \), \( f(x)=\sqrt{x} \). Determine the range of values of \( f(x) \) for \( x \in \left[-3,-\frac{5}{2}\right] \).
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