
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 the sample data $a_1$, $a_2$, $a_3$, $a_4$, $a_5$ with variance $s^2 = \frac{1}{5}(a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 - 80)$, find the mean of the sample data $2a_1 + 1$, $2a_2 + 1$, $2a_3 + 1$, $2a_4 + 1$, $2a_5 + 1$.

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