
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 a building with 300 apartments, cats live in apartments whose numbers are divisible by 5, while no cats live in the other apartments. If the sum of the digits of an apartment number is divisible by 5, a dog definitely lives there, and no dogs live in the other apartments. How many apartments have both a cat and a dog living in them?

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