
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
In the city of Perpendicularka, new multi-story houses are planned to be built, with some potentially being single-story houses, so that the total number of floors is equal to 30. The city’s architect Parallelnikov proposed a project according to which, if you climb to the roof of each new house, count the number of new houses that are shorter, and add all such numbers, the resulting sum will be maximized. What is this sum? How many houses are proposed to be built, and what are their floor counts?

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