
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. The polar equation of curve C is $\rho \sin^2\theta + 4\sin\theta - \rho = 0$, and the line $l$ is defined by the parametric equations $\begin{cases} x=2+ \frac{ \sqrt{2}}{2}t \\ y=3+ \frac{ \sqrt{2}}{2}t \end{cases}$ (where t is a parameter), which intersects curve C at points M and N.

(1) Write the Cartesian equation of curve C and the standard equation of line l.
(2) Calculate the length of the segment $|MN|$.

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