
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 $z\_1=2+i$, $\overline{z\_1} \cdot z\_2 = 6 + 2i$,
(1) Find $z\_2$;
(2) If $z = \frac{z\_1}{z\_2}$, find the modulus of $z$.

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