
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 hyperbola $\dfrac{x^2}{2}-\dfrac{y^2}{b^2}=1 \ (b > 0)$, its left and right foci are $F_1$ and $F_2$ respectively, and one of its asymptote equations is $y=x$. The point $P(\sqrt{3},y_0)$ is on the hyperbola. Calculate the dot product of vectors $\overrightarrow{PF_1}$ and $\overrightarrow{PF_2}$.

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