
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 that the conic sections $C_{1}: mx^{2}+ny^{2}=1 (n>m>0)$ and $C_{2}: px^{2}-qy^{2}=1 (p>0, q>0)$ share common foci $F_{1}$, $F_{2}$. Point $M$ is a common point of $C_{1}$ and $C_{2}$, and satisfies $\angle F_{1}MF_{2}=90^{\circ}$. If the eccentricity of the conic section $C_{1}$ is $\frac{3}{4}$, then determine the eccentricity of $C_{2}$.

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