
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 the ellipse $C_{1}: \frac{x^{2}}{m^{2}}+y^{2}=1$ ($m > 1$) and the hyperbola $C_{2}: \frac{x^{2}}{n^{2}}-y^{2}=1$ ($n > 0$) have coincident foci, determine the relationship between $m$ and $n$ and the product of the eccentricities $e_{1}$ and $e_{2}$.

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