
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
If one set is a subset of another set, they are called "full food"; if two sets have common elements but are not subsets of each other, they are called "partial food." For the sets $A=\{-1,\frac{1}{2},1\}$ and $B=\{x|ax^{2}=1,a\geqslant 0\}$, if the two sets form "full food" or "partial food," then the value of $a$ is ______.

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