
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 $f(x) = x^{3} + \frac{5}{2}x^{2} + ax + b$ (where $a, b$ are constants), with its graph being the curve $C$.

(1) When $a = -2$, find the monotonic decreasing interval of the function $f(x)$;

(2) Let the derivative of the function $f(x)$ be $f'(x)$. If there exists a unique real number $x_{0}$ such that $f(x_{0}) = x_{0}$ and $f'(x_{0}) = 0$ both hold true, find the range of values for the real number $b$;

(3) Suppose point $A$ is a moving point on curve $C$, and at point $A$, the tangent line to curve $C$ is $l_1$, which intersects $C$ at another point $B$. At point $B$, the tangent line to curve $C$ is $l_2$. Let the slopes of the tangent lines $l_1$ and $l_2$ be $k_1$ and $k_2$, respectively. Is there a constant $\lambda$ such that $k_2 = \lambda k_1$? If there is, find the value of $\lambda$; if there is not, please explain why.

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