
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 rectangular coordinate system, with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis, the curve $C: ρ\sin^2θ=2a\cos θ(a > 0)$ is given. The parametric equations of the line $l$ passing through the point $P(-2,-4)$ are $\begin{cases} x=-2+\frac{\sqrt{2}}{2}t \\ y=-4+\frac{\sqrt{2}}{2}t \end{cases} (t$ as the parameter$)$, and $l$ intersects $C$ at $M$ and $N$, respectively.
(I) Write the rectangular coordinate equation of $C$ and the general equation of $l$;
(II) If $|PM|, |MN|, |PN|$ form a geometric sequence, find the value of $a$.

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