
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 that $f(x)$ is a decreasing function defined on $R$, and for any $x, y \in R$, it holds that $f(x) + f(y) = f(x+y) + 2$. If the solution set that satisfies $f(x^{2}-ax) + f(x-a) > 4$ contains exactly two integers, then the range of real numbers for $a$ is ______.

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