
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]


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Given a set of observed data $(x_{i},y_{i})(i=1,2,…6)$ for linearly correlated variables $x$ and $y$, the regression line equation is $\hat{y}=\frac{1}{4}x+a$, where $x_{1}+x_{2}+…+x_{6}=10$ and $y_{1}+y_{2}+…+y_{6}=4$, determine the value of the real number $a$.

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