
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 $ABC$ with $\angle B = 90^\circ$, sides $AB=1$ and $BC=3$. The bisector of $\angle BAC$ meets $\overline{BC}$ at $D$. Calculate the length of segment $BD$.
A) $\frac{1}{2}$
B) $\frac{3}{4}$
C) $1$
D) $\frac{5}{4}$
E) $2$

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