
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 pet shelter housing 100 dogs, 20 dogs enjoy apples, 70 dogs enjoy chicken, and 10 dogs enjoy cheese. 7 dogs enjoy both apples and chicken, 3 dogs enjoy both apples and cheese, and 5 dogs enjoy both chicken and cheese. 2 dogs enjoy all three. How many dogs enjoy none of these foods?

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