
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 that the origin of the rectangular coordinate system is taken as the pole, the positive semi-axis of the $x$-axis is taken as the polar axis, and the same length unit is taken in both coordinate systems, the polar coordinate equation of the curve $C$ is $\rho \cos ^{2}\theta=2a\sin \theta (a > 0)$, and the parameter equation of the line $l$ is $ \begin{cases} x=-4+ \frac { \sqrt {2}}{2}t \\ y=-2+ \frac { \sqrt {2}}{2}t \end{cases} (t \text{ is the parameter}) $.
(1) Write out the ordinary equations of the curve $C$ and the line $l$;
(2) In the rectangular coordinate system $xOy$, it is known that point $P(-4,-2)$, and the line $l$ intersects with the curve $C$ at points $M$ and $N$. If $|PM|, |MN|, |PN|$ form a geometric sequence, find the value of the real number $a$.

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