
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
A community plans to organize three activities, "Book Club," "Fun Sports," and "Environmental Theme Painting," in order to enrich the lives of residents. A total of 120 people have signed up for the activities, with each resident participating in at most two activities. It is known that 80 people participate in the "Book Club," 50 people participate in "Fun Sports," and 40 people participate in "Environmental Theme Painting." Additionally, 20 people participate in both the "Book Club" and "Fun Sports," and 10 people participate in both "Fun Sports" and "Environmental Theme Painting." Find the number of people who participate in both the "Book Club" and "Environmental Theme Painting."

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