
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
The specification of paper refers to the size of the paper after it has been trimmed and cut to a certain size. Currently, China uses international standards, which stipulate that paper sizes are represented by labels such as $A\_0$, $A\_1$, $A\_2$, $B\_1$, $B\_2$, etc. The sizes of copy paper only use the $A$ series and $B$ series. The size specifications of the $A\_n (n∈N, n≤8)$ series are as follows:

1. The ratio of the width ($x$) to the length ($y$) of all sizes of paper in the $A\_0$, $A\_1$, $A\_2$, ..., $A\_8$ series is $1:√2$.
2. By cutting an $A\_0$ paper along its length into two equal parts, an $A\_1$ size is obtained. By cutting an $A\_1$ paper along its length into two equal parts, an $A\_2$ size is obtained. This process continues until the $A\_8$ size is reached. Now, there is one piece of paper each of sizes $A\_0$, $A\_1$, $A\_2$, ..., $A\_8$. If the width of the $A\_4$ paper is $2dm$, then the area of the $A\_0$ paper is ________ $dm^{2}$; the sum of the areas of these 9 pieces of paper is ________ $dm^{2}$.

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