
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 an isosceles triangle $ABC$, the side $AB$ is equal to 10, and the base $AC$ is equal to 12. The angle bisectors of angles $A$ and $C$ intersect at point $D$. Find the length of $BD$.

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