
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 line $L$ with the following parameterization:
$$\begin{cases}
x = 2 + t\cos\alpha \\
y = 1 + t\sin\alpha
\end{cases}$$
(where $t$ is a parameter, $\alpha$ is the inclination angle of the line) intersects the ellipse $\frac{x^2}{16} + \frac{y^2}{4} = 1$ at points $A$ and $B$. If point $M(2,1)$ is exactly the midpoint of the line segment $AB$, find the slope of line $L$.

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