
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 domain of the function $f(x)$ is defined as $D={x|x≠0}$, and for any $x_1$, $x_2∈D$, $f(x_1⋅x_2)=f(x_1)+f(x_2)$.
(1) Find the value of $f(1)$;
(2) Determine the even or odd property of the function $f(x)$ and provide a proof;
(3) If $f(4)=3$, $f(x-2)+f(x+1)≤3$, and $f(x)$ is an increasing function on $(0,+∞)$, find the range of real numbers $x$.

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