
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 Mezhdugrad, houses stand along one side of the street, with each house having between $1$ and $9$ floors. According to an ancient law of Mezhdugrad, if two houses on the same side of the street have the same number of floors, then, no matter how far apart they are, there must be a house with more floors between them. What is the maximum possible number of houses that can stand on one side of the street in Mezhdugrad?

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