
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 line $l$ passes through point $P(-2,-4)$ with a slope angle of $\frac{\pi }{4}$. The curve $C$ is defined as $\rho \sin^{2}\theta =2a\cos \theta (a > 0)$, and the line $l$ intersects the curve $C$ at points $M$ and $N$.

1. Find the rectangular equation of the curve $C$ and the parametric equation of the line $l$.
2. If $|PM|$, $|MN|$, and $|PN|$ form a geometric sequence, find the value of $a$.

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