
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
A point $A(-2,-4)$ outside the parabola $y^{2}=2px (p > 0)$ is connected to a line $l$: $\begin{cases} x=-2+ \frac{\sqrt{2}}{2}t \\ y=-4+ \frac{\sqrt{2}}{2}t \end{cases} (t$ is a parameter, $t \in \mathbb{R})$ intersecting the parabola at points $M_{1}$ and $M_{2}$. The distances $|AM_{1}|$, $|M_{1}M_{2}|$, and $|AM_{2}|$ form a geometric sequence.

(1) Convert the parametric equation of line $l$ into a standard form.
(2) Find the value of $p$ and the length of the line segment $M_{1}M_{2}$.

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