
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, with each edge length of 2 cm, rests on a level surface. A point source of light, situated with an angle of elevation of 45 degrees from a vertex on the top of the cube on its vertical line, illuminates the cube. The area of the shadow cast on the surface, excluding the area just beneath the cube, is 300 square cm. Calculate the greatest integer not exceeding $1000x$, where $x$ cm is the distance from the light source directly above the vertex to the cube.

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