
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 $A=\{1,2\}$, $B=\{x|(x^2+ax)(x^2+ax+2)=0\}$, let the number of elements in set $A$ be $n(A)$, and define $m(A,B) = \begin{cases} n(A)-n(B), & n(A) \geq n(B) \\ n(B)-n(A), & n(A) < n(B) \end{cases}$. If $m(A,B)=1$, then the value of the positive real number $a$ is \_\_\_\_\_\_.

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