
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 regression line equation is $\bar{y}= \frac{1}{3}x+a$, and $x_{1}+x_{2}+\ldots+x_{8}=3$, $y_{1}+y_{2}+\ldots+y_{8}=5$. Determine the value of the real number $a$.

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