
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
There are two groups of numbers. The average of the first group is 15 and the average of the second group is 21. If the average of all the numbers in both groups is 20, what is the ratio of the number of numbers in the first group to the number of numbers in the second group?

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