
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
Let the function $y=f(x)$ be defined for all real numbers, and satisfy $f(x-y)=f(x)-f(y)$, with $f(2)=1$. When $x>0$, then $f(x)>0$.
(1) Find the value of $f(0)$;
(2) Determine the parity of the function $f(x)$;
(3) If $f(x)+f(x+2)<2$, find the range of values for $x$.

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