
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
Given that line $l$ passes through point $P(2,0)$ with a slope of $\frac{4}{3}$, and intersects the parabola $y^{2}=2x$ at points $A$ and $B$. $M$ is the midpoint of segment $AB$. Find:
(1) A parametric equation of line $l$;
(2) The length of segment $PM$ ($|PM|$);
(3) The length of segment $AB$ ($|AB|$).

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