
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
The Riemann function is a special function discovered and proposed by the German mathematician Bernhard Riemann, which has a wide range of applications in advanced mathematics. The Riemann function is defined on $\left[0,1\right]$, with the analytical expression $R(x)=\left\{\begin{array}{l}\frac{1}{p},x=\frac{q}{p}(p,q \text{ are positive integers, }\frac{q}{p} \text{ is an irreducible proper fraction})\\ 0,x=0,1 \text{ or irrational numbers on }[0,1].\end{array}\right.$. If the function $f\left(x\right)$ is an odd function defined on $R$, and for any $x$, $f\left(2+x\right)+f\left(2-x\right)=0$, when $x\in \left[0,1\right]$, $f\left(x\right)=R\left(x\right)$, then $f(2022)+f(\frac{2023}{2})+f(\frac{2024}{5})=\_\_\_\_\_\_$.

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