
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 that the differentiable functions $f\left(x\right)$ and $g\left(x\right)$ have domains of all real numbers, and for any $x$, $f\left(x\right)=x\cdot g\left(x\right)+x^{2}-1$, and $f\left(1\right)=1$, find ${f'}\left(1\right)-{g'}\left(1\right)$.

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