
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 average atomic weight of naturally occurring lead is 207.2. This is (for the most part) a mixture of three types of so-called isotopes, which are the end products of different radioactive decay series, with atomic weights of 206, 207, and 208, respectively. In the mixture, there are approximately as many atoms of 208 as there are of 206 and 207 combined.

Express the approximate ratio of the numbers of the three types of lead atoms in the mixture using small whole numbers, if possible.

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