
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 $f(x)=ax^{2}-4ax+b$, where $a > 0$, it has a maximum value of $1$ and a minimum value of $-2$ in the interval $[0,1]$.

(1) Find the values of $a$ and $b$.
(2) If the inequality $f(x) > -x+m$ always holds in the interval $[-1,1]$, find the range of values for the real number $m$.

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