
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 $f(x)=x^{2}-1$, $g(x)=a|x-1|$. 

(1) If for $x \in \mathbb{R}$, the inequality $f(x) \geqslant g(x)$ always holds, find the range of the real number $a$.

(2) Find the maximum value of the function $h(x)=|f(x)| + g(x)$ in the interval $[0,1]$.

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