
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 parametric 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 $\rho\sin^{2}\theta-16\cos\theta=0$, the line $l$ intersects the curve $C$ at points $A$ and $B$, and point $P(1,3)$,
(1) Find the standard equation of line $l$ and the Cartesian coordinate equation of curve $C$;
(2) Calculate the value of $\frac{1}{|PA|}+\frac{1}{|PB|}$.

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