
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 $ABC,$ angle bisectors $\overline{AD}$ (where $D$ is on $BC$) and $\overline{BF}$ (where $F$ is on $AC$) intersect at $Q.$ If $AB = 8,$ $AC = 4,$ and $BC = 6,$ find the ratio $\frac{BQ}{QF}.$

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