
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 $a$ and $b$ are real numbers, $i$ is the imaginary unit, and they satisfy the equation $a+bi=(1+2i)(3-i)+\frac{1+i}{1-i}$.
(1) Find the values of the real numbers $a$ and $b$;
(2) If the complex number $z=(m-a)+(m-b)i$ corresponds to a point on the complex plane that lies on the line $y=2x$, find the value of the real number $m$.

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