
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
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 \( x \in \left[-3,-\frac{5}{2}\right] \).

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