
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 $xOy$, a pole coordinate system is established with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C$ is $\rho\cos^2\theta=2a\sin\theta$ ($a>0$). The parameter equation of the line $l$ passing through the point $P(-1,-2)$ is $$\begin{cases} x=-1+ \frac { \sqrt {2}}{2}t \\ y=-2+ \frac { \sqrt {2}}{2}t\end{cases}$$ ($t$ is the parameter). The line $l$ intersects the curve $C$ at points $A$ and $B$.
(1) Find the rectangular coordinate equation of $C$ and the general equation of $l$;
(2) If $|PA|$, $|AB|$, and $|PB|$ form a geometric sequence, find the value of $a$.

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