
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 $A=[-1,1]$, $B=[-2,2]$, and the function $f(x)=2x^{2}+mx-1$,
(1) Let $C$ be the solution set of the inequality $f(x)\leqslant 0$. Find the range of real number $m$ such that $C\subseteq(A\cap B)$.
(2) If $f(1-x)=f(1+x)$ holds for any $x\in R$, find the range of $f(x)$ when $x\in B$.
(3) Given $g(x)=2|x-a|-x^{2}-mx (a\in R)$, find the minimum value of $f(x)+g(x)$.

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