
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 that the function $f(x)=({{m^2}-m-1}){x^{{m^2}+m-3}}$ is a power function, for any $x_{1}$, $x_{2}\in \left(0,+\infty \right)$, and $x_{1}\neq x_{2}$, it satisfies $\frac{{f({{x_1}})-f({{x_2}})}}{{{x_1}-{x_2}}} \gt 0$. If $a$, $b\in R$, and $f\left(a\right)+f\left(b\right) \lt 0$, then $a+b \_\_\_\_\_\_0($fill in "$ \gt $", "$=$", or "$ \lt $").

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