
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
Some middle school plans to expropriate a piece of land to build an apartment with a total construction area of $a m^2$ to solve the problem of teacher housing. It is known that the land expropriation cost is $2388 \text{ yuan/m}^2$, each floor has the same building area, the area of the expropriated land is 2.5 times that of the first floor. According to the calculations made by the engineering and technical personnel, the construction costs of the first and second floors are the same, at $445 \text{ yuan/m}^2$, and for each additional floor beyond the second, the construction cost increases by $30 \text{ yuan/m}^2$. Design the number of floors for this apartment to minimize the total cost, and calculate the minimum cost. (Total cost = construction cost + land expropriation cost).

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