
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 functions $f(x)=x^{2}-1$ and $g(x)=a|x-1|$.
(1) Find the range of values for the real number $a$ such that the inequality $f(x)\geqslant g(x)$ holds true for all $x\in R$.
(2) Find the maximum value of the function $h(x)=|f(x)|+g(x)$ in the interval $[0,2]$.

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