
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 $f(x)=x^2-2ax+a+2$,

(I) If the solution set $A$ of the inequality $f(x) \leqslant 0$ is a subset of $[0,3]$, find the range of values for the real number $a$.

(II) If the function $g(x)=f(x)+|x^2-1|$ has two zero points $x\_1$, $x\_2$ ($x\_1 < x\_2$) in the interval $(0,3)$, find the range of values for the real number $a$.

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