
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 in the complex plane, the points A and B correspond to the complex numbers $z_1=2a+6i$ and $z_2=-1+i$ respectively, where the complex number representing the vector $\overrightarrow {AB}$ is denoted by $z$.

(1) Find the complex number $z$;
(2) If the point $P$ corresponding to the complex number $z$ lies on the line $y=\frac{1}{2}x$, determine the value of $a$.

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