
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 the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve C is given by: $\rho\sin^2\theta=\cos\theta$.
(1) Find the Cartesian equation of curve C;
(2) If the parametric equation of line L is $$\begin{cases} \left.\begin{matrix}x=2- \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t\end{matrix}\right.\end{cases}$$ (t is the parameter), and line L intersects curve C at points A and B, find $|AB|$.

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