
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 $s^{2}= \frac {1}{5}(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}-80)$, then the mean of the sample data $2a_{1}+1$, $2a_{2}+1$, $2a_{3}+1$, $2a_{4}+1$, $2a_{5}+1$ is ______.

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