
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 two-dimensional rectangular coordinate system, establish a polar coordinate system 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 curve $C$ is given by $ρ\sin^2θ=2a\cos θ (a > 0)$. The parametric equations of line $l$ passing through point $P(-2,-4)$ are $x=-2+\frac{\sqrt{2}}{2}t$ and $y=-4+\frac{\sqrt{2}}{2}t$, where $t$ is the parameter. Line $l$ intersects curve $C$ at points $A$ and $B$.

(I) Write the rectangular coordinate equation for curve $C$ and the standard equation for 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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