
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 the ellipse $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$, and the point $P\left( \dfrac { \sqrt {5}}{5}a, \dfrac { \sqrt {2}}{2}a\right)$ is on the ellipse.  
$(1)$ Find the eccentricity of the ellipse;  
$(2)$ Let $A$ be the left vertex of the ellipse, and $O$ be the origin. If point $Q$ is on the ellipse and satisfies $|AQ|=|AO|$, find the value of the slope of line $OQ$.

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