
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 and Parametric Equation Section) In the Cartesian coordinate system xOy, it's known that curve C1 is defined by the parametric equations $\begin{cases} x=t+2 \\ y=1-2t \end{cases}$ (with parameter $t$), and curve C2 by $\begin{cases} x=3\cos\theta \\ y=3\sin\theta \end{cases}$ (with parameter $\theta$). If they intersect at two points A and B, then the length of the segment AB is ______.

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