
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 class of 40 students, 20 students have dogs, $\frac{1}{4}$ of the students have cats, and 10 students have other types of pets. Five students don't have any pets at all. In a Venn diagram, the number of students who have only dogs is labeled as 15, only cats as 4, and only other pets as 5. The numbers of students who have exactly two types of pets are labeled as follows: dogs and cats ($x$), dogs and other pets ($y$), and cats and other pets ($z$). How many students have all three types of pets?

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