
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
Let the quadratic function $f(x) = mx^2 + nx$, and the function $g(x) = ax^3 + bx - 3$ ($x > 0$), given that $f'(0) = 0$, $f'(-1) = -2$, $f(1) = g(1)$, and $f'(1) = g'(1)$.

(1) Find the expressions for functions $f(x)$ and $g(x)$;  
(2) Determine whether there exist real numbers $k$ and $p$ such that $f(x) \geq kx + p$ and $g(x) \leq kx + p$ hold. If they exist, find the values of $k$ and $p$; if not, explain why.

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