
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 \( n+2 \) real numbers
\[ a_{1}, a_{2}, \cdots, a_{n}, 16, a_{n+2} \]
where the average of the first \( n \) numbers is 8, the average of the first \( n+1 \) numbers is 9, and the average of these \( n+2 \) numbers is 10. Find the value of \(a_{n+2}\).

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