
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
Let the origin of the Cartesian coordinate system coincide with the pole of the polar coordinate system, and the positive half-axis of the $x$-axis coincide with the polar axis. If the polar equation of curve $C$ is given by $\rho^{2}= \dfrac {12}{3\cos ^{2}\theta +4\sin ^{2}\theta }$, and points $F_{1}$ and $F_{2}$ are its left and right foci, respectively. The parametric equation of line $l$ is given by $\begin{cases} x=2+ \dfrac { \sqrt {2}}{2}t \\ y= \dfrac { \sqrt {2}}{2}t\end{cases}$ (where $t$ is the parameter, $t\in\mathbb{R}$)  
$(1)$ Find the standard equation of line $l$ and the Cartesian coordinate equation of curve $C$;  
$(2)$ Find the maximum distance from a moving point $P$ on curve $C$ to line $l$.

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