
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 plane rectangular coordinate system $(xOy)$, curve $({C_{1}})$ is given by: $\begin{cases} & x=\sqrt{2}\cos \theta \\ & y=\sqrt{3}\sin \theta \end{cases}$ $(\theta$ is a parameter$)$, and curve $({C_{2}})$ is given by: $\begin{cases} & y=-t+4\sqrt{5} \\ & x=t \end{cases}$ $(\text{where } t \text{ is a parameter})$.

(1) Write the general equations of curves $({C_{1}})$ and $({C_{2}})$;

(2) If point $P$ is on curve $({C_{1}})$, find the maximum distance from point $P$ to curve $({C_{2}})$.

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