
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 $f(x)=ax^{2}-2x+c$, and the solution set of $f(x) > 0$ is ${x|x\neq \frac {1}{a}}$.
(1) Find the minimum value of $f(2)$ and the analytic expression of $f(x)$ when $f(2)$ takes the minimum value;
(2) When $f(2)$ takes the minimum value, if for any $x > 2$, $f(x)+4\geqslant m(x-2)$ always holds, find the range of values of the real number $m$.

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