
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
A solid cube has a volume of \(1000 \ \text{cm}^3\). A cube with volume \(64 \ \text{cm}^3\) is removed from one corner of the cube. The resulting solid has a total of nine faces: three large squares that were faces of the original cube, three of the original faces with a square removed from one corner, and three smaller squares. One of the smaller square faces is shaded. The ratio of the area of the shaded face to the surface area of the new solid is of the form \(2: x\). What is the value of \(x\)?

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