
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 curve $C$: $mx^{2}+ny^{2}=1$ passes through points $A(5,0)$, $B(4, \frac {12}{5})$.

(1) Find the equation of curve $C$.

(2) If a point $P$ on curve $C$ is at a distance of $6$ from point $M(-3,0)$, find the distance between point $P$ and point $N(3,0)$, denoted as $|PN|$.

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