
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
Given a list of nine numbers, the average of the first five numbers is 7, and the average of the last five numbers is 10. If the average of all nine numbers is $8\frac{2}{9}$, determine the number common to both sets of five numbers.

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