
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 $f\left(x\right)=$____ with the following properties:<br/>① The domain of $f\left(x\right)$ is $\left(0,+\infty \right)$;<br/>② $f(x_{1}x_{2})=f(x_{1})+f(x_{2})$;<br/>③ When $x\in \left(0,+\infty \right)$, ${f'}\left(x\right) \lt 0$.

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