
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 observational data $(x_i,y_i)$ ($i=1,2,…,8$) for variables $x$ and $y$ that have a linear relationship, the equation of the regression line is $\hat{y}= \frac{1}{3}x + a$. If $x_1+x_2+…+x_8=3$ and $y_1+y_2+…+y_8=5$, find the value of the real number $a$.

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