
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
The number \( x+\sqrt{y} \) and its radical conjugate have a sum of \( 6 \) and a product of \( 9 \). Find \( x+y \).

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