
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 city adopts a lottery system for "price-limited housing," where winning families can randomly draw a house number from the available housing in a designated community. It is known that two friendly families, Family A and Family B, have both won the lottery and decided to go together to a certain community to draw their house numbers. Currently, there are $5$ houses left in this community, spread across the $4^{th}$, $5^{th}$, and $6^{th}$ floors of a building, with $1$ house on the $4^{th}$ floor and $2$ houses each on the $5^{th}$ and $6^{th}$ floors.

(Ⅰ) Calculate the probability that Families A and B will live on the same floor.

(Ⅱ) Calculate the probability that Families A and B will live on adjacent floors.

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