
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 $g\left(x\right)=x^{2}f\left(x\right)$, the derivatives of $f\left(x\right)$ and $g\left(x\right)$ are denoted as ${f'}\left(x\right)$ and ${g'}\left(x\right)$, respectively. If $f\left(1\right)={f'}\left(1\right)=2$, then find the value of ${g'}\left(1\right)$.

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