
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, it is known that $\frac{1}{2}$ of the students have a dog, $\frac{2}{5}$ have a cat, 8 students have a different type of pet, and 7 students have no pets at all. The Venn diagram details are as follows: 12 students only have dogs, 3 students have both dogs and other pets but no cats, and 11 students only have cats. How many students have all three types of pets?

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