
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 $f(x)=ax^3+bx^2+cx$, it attains extreme values at $x=1$ and $x=-3$, and $f(1)=-5$:
1. Find the explicit form of the function.
2. If the function is monotonically increasing in the interval $[m, m+1]$, determine the range of values for $m$.
3. If the equation $f(x)=a$ has at least two different real roots, determine the range of values for $a$.

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