
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 $ABC$, where $\angle B$ is an obtuse angle, $CD$ is the altitude to $AB$ and $AE$ is the altitude to $BC$. Given that $AB = 13$, $CD = 5$, and $AE = 12$, find the length of $DB$. Note: Portions $DB$ and $DC$ are split by altitude $CD$, and $D$ lies on $AB$.
A) $\frac{15}{13}$
B) $\frac{65}{13}$
C) $\frac{65}{12}$
D) $\frac{25}{12}$
E) $\frac{80}{13}$

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