
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
Triangle $ABC$ is a right triangle with $AB = 6$, $BC = 8$, and $AC = 10$. Point $D$ is on line $\overline{BC}$ such that $\overline{AD}$ bisects angle $BAC$. The inscribed circles of $\triangle ADB$ and $\triangle ADC$ have radii $r_1$ and $r_2$, respectively. What is $r_1/r_2$?
A) $\frac{24}{35}$
B) $\frac{35}{24}$
C) $\frac{15}{28}$
D) $\frac{7}{15}$

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