
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 $f(x)=x^{2}+ax+b(a,b∈R)$ with a range of $[0,+∞)$, the solution set of the inequality $f(x) < m$ with respect to $x$ is $(c,c+2 \sqrt {2})$.
(1) Find the value of the real number $m$;
(2) If $x > 1$, $y > 0$, $x+y=m$, find the minimum value of $\frac {1}{x-1}+ \frac {2}{y}$.

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