
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
With the origin of the Cartesian coordinate system as the pole and the positive half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C_{1}$ is $\rho\sin (\theta- \dfrac {\pi}{4})= \sqrt {2}$, and the polar equation of curve $C_{2}$ is $\rho=2\cos (\theta- \dfrac {\pi}{4})$.
$(1)$ Write the standard equation of curve $C_{1}$ and the parametric equation of curve $C_{2}$;
$(2)$ Let $M$ and $N$ be two points on curves $C_{1}$ and $C_{2}$, respectively. Find the minimum value of $|MN|$.

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