
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
Given a circle is inscribed in a triangle with side lengths $9, 12$, and $15$, let the segments of the side of length $9$, made by a point of tangency, be $p$ and $q$, with $p < q$. Calculate the ratio $p:q$.

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