
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
A line defined by the parameterized equations $x=1+t$ and $y=-2+t$ intersects the ellipse defined by the equation $x^{2}+2y^{2}=8$ at points $A$ and $B$. Find the length of segment $|AB|$.

A) $2\sqrt{2}$
B) $\frac{4\sqrt{3}}{3}$
C) $2$
D) $\frac{\sqrt{6}}{3}$

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