
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
Define $A \otimes B = \{z | z = xy + \frac{x}{y}, x \in A, y \in B\}$. Let the set $A = \{0, 2\}$, and the set $B = \{1, 2\}$. (1) Find the sum of all elements in the set $A \otimes B$. (2) List all proper subsets of the set $A \otimes B$.

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