
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 an ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$, the distance from its right focus to the line $x-y+3 \sqrt {2}=0$ is $5$, and the distance between one endpoint of the major axis and one endpoint of the minor axis of the ellipse $C$ is $\sqrt {10}$.

(1) Find the standard equation of the ellipse $C$;

(2) Given the point $Q( \frac {6 \sqrt {5}}{6},0)$, for any chord $AB$ of the ellipse $C$ passing through $Q$, is $\frac {1}{|QA|^{2}}+ \frac {1}{|QB|^{2}}$ a constant value? If yes, find this constant value, if not, explain the reason.

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