
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
Write a function $f\left(x\right)=$____ that simultaneously satisfies the following properties:①②③.<br/>①$f\left(x+4\right)=f\left(x\right)$；②For all $x_{1}$,$x_{2}\in \left[0,1\right]$, $\frac{{f({{x_1}})-f({{x_2}})}}{{{x_1}-{x_2}}}＜0$；③$f\left(x\right)$ is an odd function.

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