
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
For an ellipse given by $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ with three distinct points $A\left(x_{1}, y_{1}\right), B\left(4, \frac{9}{5}\right), C\left(x_{2}, y_{2}\right)$ on it, the distances from these points to the right focus of the ellipse form an arithmetic sequence. The perpendicular bisector of segment $A C$, denoted as $l$, intersects the X-axis at point $T$. Find the equation of the line $B T$.

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