
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 $C:\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1(a > b > 0)$ and a line $y=x+3$ have only one common point, and the eccentricity of the ellipse is $\dfrac{\sqrt{5}}{5}$, then the equation of the ellipse $C$ is \_\_\_\_.

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