
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 the sets $S=\{x|x^2-px+q=0\}$, $T=\{x|x^2-(p+3)x+6=0\}$, and $S \cap T=\{3\}$  
(1) Find the value of $\log_{9}(3p+q)$;  
(2) Find $S \cup T$.

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