
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
There are  $522$  people at a beach, each of whom owns a cat, a dog, both, or neither. If  $20$  percent of cat-owners also own a dog,  $70$  percent of dog-owners do not own a cat, and  $50$  percent of people who don’t own a cat also don’t own a dog, how many people own neither type of pet?

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