
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 $f(x)=\frac{1}{(|x-1|-a)^{2}}$ with domain $D$, where $a<1$.
(1) Write the monotonic intervals of the function $f(x)$ when $a=-3$ (proof is not required);
(2) If for any $x\in[0,2]\cap D$, the inequality $f(x)\geqslant kx^{2}$ holds, find the range of values for the real number $k$.

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