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

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