
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, a coordinate system is established with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Given the curve $C$: $ρ\sin ^{2}θ=2a\cos θ(a > 0)$, and the parametric equations of line $l$ passing through point $P(-2,-4)$ is $ \begin{cases} x=-2+t \\ y=-4+t\\end{cases}$, where line $l$ intersects curve $C$ at points $M$ and $N$.

1. Write the ordinary equations of curve $C$ and 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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