
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
In the Cartesian coordinate system xOy, a polar coordinate system is established with the origin O as the pole and the positive half-axis of the x-axis as the polar axis. It is known that the ray at $\theta = \frac{\pi}{4}$ intersects the curve given by the parametric equations $\begin{cases} x=t+1 \\ y=(t-1)^2 \end{cases}$ (with t as the parameter) at points A and B. Find the Cartesian coordinates of the midpoint of segment AB.

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