
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 small pyramid with a square base of side 2 centimeters is placed on a horizontal surface. It is illuminated by a point source of light located $y$ centimeters above one of the vertices of the square base. The shadow of the pyramid, excluding the area right beneath it, measures 36 square centimeters. Determine the highest integer less than or equal to $800y$.

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