
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 $z=1+mi$, where $i$ is the imaginary unit and $m\in\mathbb{R}$, and $\overline{z}\cdot (3+i)$ is a pure imaginary number ($\overline{z}$ is the complex conjugate of $z$).
1. Let $z_1=\frac{m+2i}{1-i}$, find $|z_1|$.
2. Let $z_2=\frac{a-i^{2017}}{z}$, and the point corresponding to the complex number $z_2$ is in the first quadrant, find the range of values for the real number $a$.

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