
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 the parameterized equation of line $l$ as $\begin{cases}x=1+t \\ y=3+2t\end{cases} (t\text{ is a parameter})$, and the polar coordinate equation of curve $C$ as $p{\sin }^{2}\theta -16\cos \theta =0$, line $l$ intersects curve $C$ at points $A$ and $B$, and point $P(1,3)$.

(1) Find the standard form equation of line $l$ and the rectangular coordinate equation of curve $C$.

(2) Find the value of $\frac{1}{\left|PA\right|}+ \frac{1}{\left|PB\right|}$.

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