
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
The polar coordinate system is established in the plane with the origin as the pole and the positive x-axis as the polar axis. The polar equation of curve C is $\rho\sin^2\theta=2a\cos\theta$ ($a>0$). The parametric equation of the line l passing through the point P $(-2, -4)$ is
$$
\begin{cases}
x = -2 + \frac{\sqrt{2}}{2}t \\
y = -4 + \frac{\sqrt{2}}{2}t
\end{cases}
$$
($t$ is the parameter), and the line l intersects with curve C at points A and B.
(I) Write the rectangular coordinate equation of curve C and the ordinary equation of line l.
(II) If $|PA| \cdot |PB| = |AB|^2$, find the value of $a$.

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