
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]


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The function $f(x)=(m^2-m-1)x^{4m^9-m^5-1}$ is a power function. For any $x_1$, $x_2 \in (0, +\infty)$, and $x_1 \neq x_2$, it satisfies $\frac{f(x_1)-f(x_2)}{x_1-x_2} > 0$. If $a$, $b \in \mathbb{R}$, and $a+b > 0$, then the value of $f(a)+f(b)$:

① Always greater than $0$;

② Always less than $0$;

③ Equals to $0$;

④ Cannot be determined.

The correct conclusion is __________ (fill in the serial number).

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