
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 two sets $A=\{1, 2, 3\}$ and $B=\{2, 3\}$. Define the operation "$*$" between sets $A$ and $B$ as $A*B=\{x | x=x_1+x_2, x_1 \in A, x_2 \in B\}$. Determine the largest element in the set $A*B$ and the number of all proper subsets of $A*B$.

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