
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 the complex number $z= \frac {3+i}{2-i}$, and $z_1=2+mi$,
(1) If $|z+z_1|=5$, find the value of the real number $m$;
(2) If the point corresponding to the complex number $az+2i$ in the complex plane lies in the second quadrant, find the range of the real number $a$.

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