
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, a polar coordinate system is established with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Given the curve $C:ρ\sin^2θ=2a\cos θ (a > 0)$, the line $l:\begin{cases}x=-2+\frac{\sqrt{2}}{2}t\\y=-4+\frac{\sqrt{2}}{2}t\end{cases} (t$ is the parameter$) $ passes through point $P(-2,-4)$ and intersects curve $C$ at points $M$ and $N$.

(I) Find the ordinary equations of curve $C$ and line $l$;

(II) If $|PM|, |MN|, |PN|$ form a geometric sequence, find the value of real number $a$.

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