
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 edges two centimeters long is placed on a horizontal surface. A point source of light located $y$ centimeters directly above one of the cube's upper vertices illuminates it. This setup results in the cube casting a shadow on the horizontal surface, excluding the area right beneath the cube, which totals 324 square centimeters. Determine the largest integer less than or equal to $500y$.

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