
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
For a set of observed data $(x_i, y_i) i = (1,2,...,8)$ of variables $x$, $y$ that have a linear relationship, the regression line equation is $\bar{y}= \frac{1}{3}x+ \bar{a}$. Given that $x_1+x_2+x_3+...+x_8=2(y_1+y_2+y_3+...+y_8)=6$, determine the value of the real number $a$.

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