
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. It is known that the polar equation of curve C is $\rho=2\sqrt{2}\sin(\theta+\frac{\pi}{4})$. A line $l$, which has an inclination angle of $\frac{\pi}{3}$ and passes through the fixed point P(0,1), intersects curve C at points M and N.  
(I) Write the standard form of the parametric equation of line $l$ and find the Cartesian equation of curve C;  
(II) Calculate the value of $\frac{1}{|PM|}+\frac{1}{|PN|}$.

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