
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 on the plane, establish a polar coordinate system $(.$ with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Given the curve $C$: $ρ\cos^2θ=2a\sinθ (a > 0)$, and the parameter equation of line $l$ is $\begin{cases}x=-4+\frac{\sqrt{2}}{2}t\\y=-2+\frac{\sqrt{2}}{2}t\end{cases} (t)$ (where $(t)$ is the parameter).

Line $l$ intersects curve $C$ at points $M$ and $N$, respectively.

(1) Write the rectangular coordinate equation of $C$ and the general form equation of $l$;

(2) Set point $P(-4,-2)$, 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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