
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 function $f(x)$ satisfies the equation $f(x+y)-f(y)=(x+2y+2)x$ for all real numbers $x$ and $y$, and $f(2)=12$.

1. Find the value of $f(0)$.
2. There exists a real number $x\_0\in R$ in the interval $(1,4)$ such that $f(x\_0)-8=ax\_0$ holds. Find the range of values for the real number $a$.

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