
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 that $F_1$ and $F_2$ are the left and right foci of the ellipse $\frac{x^2}{4} + \frac{y^2}{3} = 1$, and point $P(x, y)$ is on the line $y - x - 3 = 0$ $(x \neq -3$ and $x \neq \pm \sqrt{3})$, find the value of $\frac{1}{k_2} - \frac{2}{k_1}$.

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