
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
Make a rectangular box with a volume of $32m^{3}$ and a height of $2m$.  
$(1)$ If $x$ represents the length of one side of the base of the rectangular box, and $S$ represents the surface area of the rectangular box, write the function relationship of $S$ with respect to $x$;  
$(2)$ What value of $x$ should be taken to use the least amount of paper to make such a rectangular box? How much paper is used at the minimum in $m^{2}$?

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