
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
The mean of one set of three numbers is 15, and the mean of a separate set of five numbers is 20. Additionally, it is known that the largest number in the first set is equal to the smallest number in the second set, which is 12. Find the mean of the set of all eight numbers.

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