
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 the linear correlation variables $x$ and $y$ with observed data $(x_i, y_i)$ ($i=1, 2, ..., 15$), their linear regression equation is $\hat{y} = 5x + 11$, where $\sum_{i=1}^{15} x_i = 18$. Determine the value of $\sum_{i=1}^{15} y_i$.

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