
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 $a$, $b$, $c \in \mathbb{R}$, the function $f(x) = x^3 + ax^2 + bx + c$ attains extreme values at $x=1$ and $x=3$,
1. Determine the values of $a$ and $b$;
2. If the equation $f(x)=0$ has three distinct real roots, find the range of possible values for $c$.

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