
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
Consider an ellipse (E) with the equation $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$, having one of its foci at $F_1(-2,0)$ and an eccentricity of $e = \dfrac{1}{2}$.
(1) Find the equation of the ellipse (E);
(2) Determine the equation of the line on which the chord AB lies, where P(2,1) is the midpoint of AB.

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