
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 $f(x)=ax^3+bx$.

(Ⅰ) If the tangent line to the function $f(x)$ at $x=3$ is parallel to the line $24x-y+1=0$, and the function $f(x)$ has an extremum at $x=1$, find the function $f(x)$ and its interval of monotonic decrease.

(Ⅱ) If $a=1$, and the function $f(x)$ is decreasing on the interval $[-1,1]$, find the range of the real number $b$.

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