
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 differentiable functions $f\left(x\right)$ and $g\left(x\right)$, where $f\left(1\right)=-1$, $f'\left(1\right)=2$, $g\left(1\right)=-2$, and $g'\left(1\right)=1$, calculate the value of the derivative of $f\left(x\right)\cdot g\left(x\right)$ at $x=1$.

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