
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
In the Cartesian coordinate system $xOy$, the general equation of curve $C_{1}$ is $C_{1}$: ${x^2}+\frac{{y^2}}{3}=1$, and the polar coordinate equation of curve $C_{2}$ is: $\rho =2\cos \theta +4\sin \theta $. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive x-axis as the polar axis.<br/>$(1)$ Find the parametric equations of curve $C_{1}$ and the general equation of curve $C_{2}$;<br/>$(2)$ If the curve $θ=\frac{π}{4}(ρ＞0)$ intersects curves $C_{1}$ and $C_{2}$ at points $M$ and $N$ respectively, find $|MN|$.

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