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

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