
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 real estate developer determines the price of a 23-story building before sale using the following method: Since both the first and the top floors are duplex structures, the price of the first floor is $a_1$ yuan/$m^2$, and due to the better view, the top floor's price is $a_2$ yuan/$m^2$. The price of the second floor is $a$ yuan/$m^2$. Starting from the third floor, the price increases by $\dfrac{a}{100}$ yuan/$m^2$ for each floor above the previous one. The average price per square meter for this building is $\boxed{\text{answer}}$ yuan/$m^2$.

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