
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 that variables $x, y$ are linearly related, and the regression line equation is $\hat y= \frac {1}{4}x+a$, with the given sums $x_1+x_2+\ldots+x_6=10$ and $y_1+y_2+\ldots+y_6=4$, calculate the value of the real number $a$.

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