
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 $f(x)=x^{2}+(x-1)|x-a|$.
(1) If $a=-1$, solve the equation $f(x)=1$;
(2) If the function $f(x)$ is strictly increasing on $\mathbb{R}$, determine the range of values for the real number $a$;
(3) If $a < 1$ and the inequality $f(x)\geqslant 2x-3$ holds for all real numbers $x\in\mathbb{R}$, determine the range of values for $a$.

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