
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
The common foci of the ellipse $\frac{x^{2}}{6} + \frac{y^{2}}{2} = 1$ and the hyperbola $\frac{x^{2}}{3} - y^2 = 1$ are $F_1$ and $F_2$. If P is a point of intersection of the two curves, then the value of $\cos\angle F_1PF_2$ is ______.

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