
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 complex numbers $z\_1=\frac{3}{a}+(10-a^{2})i$ and $z\_2=\frac{2}{1-a}+(2a-5)i$, where $a > 0$, if $\overline{z\_1}+z\_2$ is a real number,

(1) Find the value of real number $a$;

(2) Find the magnitude of $\frac{z\_1}{z\_2}$.

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