
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 $z=(2+i)m^{2}- \frac{6m}{1-i}-2(1-i)$ (where $i$ is the imaginary unit), for what value(s) of the real number $m$ is the complex number $z$  
(Ⅰ) purely imaginary;  
(Ⅱ) a complex number corresponding to a point on the bisector of the second and fourth quadrants in the complex plane.

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