
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
The standard equation of an ellipse with foci on the x-axis, a sum of major and minor axes of 10, and a focal distance of $4 \sqrt {5}$ is $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$, where $a$ and $b$ are the semi-major and semi-minor axes, respectively.

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