
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 polyhedron $ABCD-A_{1}B_{1}C_{1}D_{1}$ is a regular quadrangular prism, where the ratio of the areas of the top and bottom faces is $1:16$. The height of the prism is three times the length of the side of the top face. Find the approximate surface area of the prism given that the volume of the prism is $567m^{3}$.

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