
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 ellipse $C_{1}: \dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ and hyperbola $C_{2}: x^{2}-y^{2}=4$ have the same right focus $F_{2}$. Point $P$ is a common point of $C_{1}$ and $C_{2}$. If $|PF_{2}|=2$, then the eccentricity of the ellipse $C_{1}$ equals \_\_\_\_\_\_.

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