
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 set \( I = \{1, 2, \ldots, 2020\} \):
$$
\begin{array}{l}
W = \{w(a, b) = (a + b) + ab \mid a, b \in I\} \cap I, \\
Y = \{y(a, b) = (a + b) \cdot ab \mid a, b \in I\} \cap I, \\
X = W \cap Y,
\end{array}
$$

where \( W \) is the 'Wu' set, \( Y \) is the 'Yue' set, and \( X \) is the 'Xizi' set. Find the sum of the maximum and minimum numbers in the set \( X \).

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