
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
Given the polar coordinate equation of curve C as $p^{2}+2 \sqrt{2}p\cos \left(\theta+ \dfrac{\pi}{4}\right)=2$, and line $l:\theta =\alpha (\alpha \in \left[ 0,\pi \right))$, $\rho \in R)$ intersects curve C at points M and N. Establish a Cartesian coordinate system with the pole O as the origin and the polar axis as the non-negative $x$-axis.

(I) Find the parametric equation of curve C;
(II) Let P be the midpoint of line segment MN, and if $|OP|\leqslant \lambda$ always holds true, find the range of real number values for $\lambda$.

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