
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
Seven children sit in a circle. The teacher distributes pieces of candy to the children such that:

- Every child gets at least one piece of candy.
- No two children receive the same number of pieces of candy.
- The numbers of candy pieces given to any two adjacent children have a common factor other than 1.
- There is no prime dividing every child's number of candy pieces.

What is the smallest number of pieces of candy that the teacher must have ready for the children?

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