
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 points $F_{1}$ and $F_{2}$ are the common foci of the ellipse $C_{1}: \dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1$ (with $a > b > 0$) and the hyperbola $C_2: \dfrac {x^{2}}{a'^{2}}- \dfrac {y^{2}}{b'^{2}}=1$ (with $a' > 0, b' > 0$), point $P$ is an intersection point of the two curves and satisfies $\angle F_{1}PF_{2}=90^{\circ}$. Let the eccentricities of the ellipse and hyperbola be $e_{1}$ and $e_{2}$ respectively, then find the value of $\dfrac {1}{e_{1}^{2}}+ \dfrac {1}{e_{2}^{2}}$.

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