
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
Let the common foci of the ellipse $\dfrac{x^2}{10} + y^2 = 1$ and the hyperbola $\dfrac{x^2}{8} - y^2 = 1$ be $F_1$ and $F_2$, respectively. If $P$ is a point of intersection of these two curves, then the radius of the circumcircle of $\triangle PF_1F_2$ is ______.

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