
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 containing seven numbers is 15, and the mean of another set containing eight numbers is 21. If an additional number is included in the first set, making the mean of the augmented set 16, what is the mean of all the numbers combined in both sets?

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