
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 wooden cube, whose edges are two centimeters long, rests on a horizontal surface. It is illuminated by a point source of light that is $x$ centimeters directly above one of the upper vertices of the cube. The area of the shadow cast on the horizontal surface outside the area underneath the cube is 147 square centimeters. Find the greatest integer that does not exceed $1000x$.

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