
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 cylinder with a base radius of 1 cm and a height of 1 cm, rests vertically on a horizontal surface. It is illuminated by a point source of light that is $x$ centimeters directly above the center of the top face of the cylinder, generating a shadow on the horizontal surface. The total area of the shadow, excluding the area beneath the cylinder, is 75 square centimeters. Find the greatest integer that does not exceed $500x$.

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