
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 \(xOy\), the line \(y=x\) intersects with the curve represented parametrically as 
\[\begin{cases}
x=t-1 \\
y=t^{2}-1
\end{cases}\]
(where \(t\) is the parameter) at points \(A\) and \(B\). Find the length of segment \(AB\).

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