
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 data pairs (3,y_{1}), (5,y_{2}), (7,y_{3}), (12,y_{4}), (13,y_{5}) corresponding to variables x and y, the linear regression equation obtained is \hat{y} = \frac{1}{2}x + 20. Calculate the value of \sum\limits_{i=1}^{5}y_{i}.

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