
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
Let b be a real number randomly selected from the interval $[-9,27]$. Then, m and n are two relatively prime positive integers such that m/n is the probability that the equation $x^4+9b^2=(6b^2-18b)x^2$ has $\textit{at least}$ two distinct real solutions. Find the value of $m+n$.

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