
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
1. Given the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1$ with foci on the $x$-axis, where $a=6$ and $e=\frac{1}{3}$, find the standard equation of the ellipse.
2. Given that the major axis of ellipse $C$ has a length of $10$ and a focal distance of $6$, find the standard equation of ellipse $C$.

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