
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 $f(x)=x^{2}-2ax+a+2$,
(1) Denote the maximum value of $f(\sin x)$, $x\in R$ as $M(a)$, find $M(a)$;
(2) If $g(x)=f(x)+|x^{2}-1|$ has two zeros $x_{1}$, $x_{2}(x_{1} < x_{2})$ in the interval $(0,3)$, find the range of values for the real number $a$.

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