
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 quadratic function $f(x)=x^{2}+bx+c$, it is always true that $f(x)=f(2-x)$ when $x \in R$, and $3$ is a zero point of $f(x)$.

(I) Find the analytic expression of function $f(x)$;
(II) Let $g(x)=f(a^{x}) (a > 1)$, if the maximum value of function $g(x)$ on the interval $[-1,1]$ is equal to $5$, find the value of real number $a$.

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