
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 sepected from the interval  $[-17,17]$ .  Then,  $m$  and  $n$  are two relatively prime positive integers such that  $m/n$  is the probability that the equation \[x^4+25b^2=(4b^2-10b)x^2\] has  $\textit{at least}$  two distinct real solutions.  Find the value of  $m+n$ .

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