
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

The city is represented as a rectangular grid, with a five-story building in each cell. The renovation law allows you to select two adjacent cells (sharing a side) that contain buildings and demolish the building with fewer stories (or the same number of stories). Additionally, the remaining building is increased in height by the number of stories of the demolished building. What is the minimum number of buildings that can remain in the city, using the renovation law, if the city has dimensions

a) $20 \times 20$ cells;

b) $50 \times 90$ cells?

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