
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 $\triangle ABC$, let $AB=6$, $BC=7$, $AC=4$, and $O$ be the incenter of $\triangle ABC$. If $\overrightarrow{AO} = p\overrightarrow{AB} + q\overrightarrow{AC}$, determine the value of $\frac{p}{q}$.

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