
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 left focus of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$ is $F$, and $O$ is the origin. Suppose a line passing through point $F$ and not perpendicular to the coordinate axes intersects the ellipse at points $A$ and $B$. The perpendicular bisector of segment $AB$ intersects the $y$-axis at $G$. The range of the $y$-coordinate of $G$ is \_\_\_\_\_\_\_.

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