
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
We want to build a prism-shaped cement storage facility. The base is formed from a square with side lengths of $2 \mathrm{~m}$ such that two of the vertices of the base lie on one diagonal and the other two vertices lie on the other diagonal of the square. The height of the prism is $2 \mathrm{m}$. The cost of construction for the foundation, roof, and walls is $1000 \mathrm{Ft}$ per $\mathrm{m}^{2}$, and the built storage facility is valued at $2500 \mathrm{Ft}$ per $\mathrm{m}^{3}$. How should we design the base to maximize the profit from the construction?

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