
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 variables \\(x\\) and \\(y\\) that have a linear relationship, the regression equation is \\(y = \frac{1}{6}x+a\\), with \\(x_{1}+x_{2}+x_{3}+…+x_{8}=6\\) and \\(y_{1}+y_{2}+y_{3}+…+y_{8}=9\\). Find the value of the real number \\(a\\).

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