
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
In the Cartesian coordinate system $xOy$, it is known that the vertices of $\triangle ABC$ are $A(-4,0)$ and $C(4,0)$, and vertex $B$ is on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$. Find the value of $\frac{\sin A+\sin C}{\sin B}$.

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