
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
Let $\triangle ABC$ be an isosceles triangle with $AB = AC = 6$ and $BC = 8$. If $I$ is the incenter of $\triangle ABC$, what is the length of $BI$? Express your answer in the form $a + b\sqrt{c}$, where $a, b, c$ are integers, and $c$ is not divisible by any perfect square other than $1$.

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