
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 $z_{1}= \frac {2a}{a-1}+(a^{2}-1)i$ and $z_{2}=m+(m-1)i$ (where $i$ is the imaginary unit, $a$, $m \in \mathbb{R}$):

$(1)$ If $z_{1}$ is a real number, find the value of $a$;  
$(2)$ Under the condition of $(1)$, if $|z_{1}| < |z_{2}|$, find the range of values for the real number $m$.

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