
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 $f\left(x\right)=12-x^{2}$.  
$(Ⅰ)$ Find the equation of the tangent line with a slope of $-2$ to the curve $y=f\left(x\right)$;  
$(Ⅱ)$ Let $S \left(t\right)$ be the area of the triangle formed by the tangent line to the curve $y=f\left(x\right)$ at the point $\left(t,f\left(t\right)\right)$ and the coordinate axes. Find the minimum value of $S\left(t\right)$.

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