
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 $f\left(x\right)={x}^{2}$, $g\left(x\right)=\left\{\begin{array}{c}f\left(x\right),x≥0\\-f(-x),x＜0\end{array}\right.$, find the range of $x$ for which $g\left(x\right)\leqslant 2-x$ is true.

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