
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 $m \in \mathbb{R}$, the complex number $z= \frac {m(m-1)}{m+1}+(m^{2}+2m-3)i$.

(1) If $z$ is a pure imaginary number, find the value of $m$;  
(2) For what value of $m$ is the point corresponding to $z$ on the line $x+y+3=0$?

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