
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 \( \triangle ABC \), \( AB = BC = 2 \) and \( AC = 3 \). Let \( O \) be the incenter of \( \triangle ABC \). If \( \overrightarrow{AO} = p \overrightarrow{AB} + q \overrightarrow{AC} \), find the value of \( \frac{p}{q} \).

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