
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 that $f(x)$ is an odd function defined on $\mathbb{R}$, $f(x+2)$ is an even function, and for any $x_{1}$, $x_{2} \in (0,2)$, $x_{1} \neq x_{2}$, we have $\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0$. Find the function that satisfies the above conditions, and write down its analytical expression $f(x)=\_\_\_\_\_\_$.

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