
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 $f(x) = (m^2+2m)x^{m^2+m-1}$, for what value(s) of $m$ does:  
(Ⅰ) $f(x)$ become a power function;  
(Ⅱ) $f(x)$ become a direct proportionality function;  
(Ⅲ) $f(x)$ become an inverse proportionality function.

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