
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 function $f(x)=(m^{2}+2m)x^{m^{2}+m-1}$, determine the value(s) of $m$ for which $f(x)$ is:
(1) a direct proportional function?
(2) an inverse proportional function?
(3) a quadratic function?
(4) a power function?

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