
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 a common focus $F\_1$, $F\_2$ of an ellipse and a hyperbola, their eccentricities are $e\_1$, $e\_2$ respectively. Point A is a common point on both curves and satisfies ∠$F\_1AF\_2$=90°. Find the value of $$\frac {1}{e_{1}^{2}}+ \frac {1}{e_{2}^{2}}$$.

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