
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 the function $f(x)$ for any $x$, $y \in \mathbb{R}$, $f(x+y)=f(x)+f(y)$, and when $x > 0$, $f(x) > 0$  
$(1)$ Find the value of $f(0)$;  
$(2)$ Determine the parity of the function $f(x)$;  
$(3)$ If it is known that $f(1)=2$, determine the monotonicity of the function $f(x)$, and find the value of the real number $a$ that satisfies $f(2-a)=6$.

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