
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
(The full score for this question is 12 points)  
Given the function $f(x)=x^3-ax-1$,  
(1) If the function $f(x)$ is monotonically increasing on $\mathbb{R}$, find the range of the real number $a$.  
(2) If the function $f(x)$ is monotonically decreasing on the interval $(-1,1)$, find the range of the real number $a$.

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