
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
Sixteen boys went fishing. It is known that every boy who wore boots also wore a cap. Ten boys did not wear boots, and two boys did not wear caps. Which boys are more, and by how much: those who wore a cap but no boots, or those who wore boots? Be sure to explain your answer.

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