
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
If the focus $F$ of the curve $C_1$: $y^2=2px(p > 0)$ happens to be the right focus of the curve $C_2$: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a > 0,b > 0)$, and the line connecting the intersection points of $C_1$ and $C_2$ passes through point $F$, determine the eccentricity of the curve $C_2$.

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