
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 set of positive numbers $(x\_1)$, $(x\_2)$, $(x\_3)$, $(x\_4)$ with a variance of $S^{2}= \frac{1}{4} (x\_1^{2}+x\_2^{2}+x\_3^{2}+x\_4^{2}-16)$, find the average of the data set $(x\_1+3)$, $(x\_2+3)$, $(x\_3+3)$, $(x\_4+3)$.

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