
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 the universal set \( I=\{1,2, \cdots, 2020\} \). Define the sets of positive integers as follows:
\[
\begin{array}{l}
W=\{w(a, b)=(a+b)+ab \mid a, b \in \mathbb{Z}_{+}\}, \\
Y=\{y(a, b)=(a+b) \cdot ab \mid a, b \in \mathbb{Z}_{+}\},
\end{array}
\]
which are called the "Wu" set and the "Yue" set, respectively. The intersection of these two sets, denoted by \( X \), is called the "Xizi number set": \( W \cap Y=X \). The elements in the set \( X \) are called "Xizi numbers". For example,
\[
\begin{array}{l}
54=w(4,10)=y(3,3), \\
56=w(2,18)=y(1,7),
\end{array}
\]
which means that 54 and 56 are both Xizi numbers.

1. Find the sum of the maximum and minimum elements in the Xizi number set.
2. If a number \( n \) has at least two representations as \( y(a, b) \), it is called an "excellent number". For example, 30 is an excellent number because \( 30=y(1,5)=y(2,3) \). How many excellent numbers are there in the set \( Y \)?

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