
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 $\triangle ABC$, $AB=8$, $BC=13$, $AC=10$, and $D$ is on $\overline{BC}$ such that $AD=8$. Find the ratio of $BD:DC$.
A) $\frac{5}{13}$  
B) $\frac{36}{133}$  
C) $\frac{133}{36}$  
D) $\frac{7}{19}$  
E) $\frac{2}{13}$

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