
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 variables $x$ and $y$ that have a linear relationship, there is a set of observation data $(x_i, y_i)$ ($i=1,2,\ldots,8$), and their regression line equation is $\hat{y} = \frac{1}{3}x + \hat{a}$. Given that $x_1+x_2+x_3+\ldots+x_8 = 2(y_1+y_2+y_3+\ldots+y_8) = 8$, please estimate the value of $y$ when $x=3$.

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