
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 right triangle $ABC$, legs $AB = 5$ cm and $BC = 12$ cm. Compute the length of the longer angle trisector extending from vertex $B$ to the hypotenuse $AC$.
**A)** $\frac{98}{12}$
**B)** $\frac{119\sqrt{3}}{36}$
**C)** $\frac{25}{12} + \frac{119\sqrt{3}}{36}$
**D)** $\frac{12\sqrt{3}}{25}$
**E)** $\frac{144}{119}$

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