
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 \( a_{1}, a_{2}, \cdots, a_{20} \in \{1,2, \cdots, 5\} \) and \( b_{1}, b_{2}, \cdots, b_{20} \in \{1,2, \cdots, 10\} \). Define the set \( X = \left\{(i, j) \mid 1 \leq i < j \leq 20, \left(a_{i} - a_{j}\right)\left(b_{i} - b_{j}\right)<0\right\} \). Find the maximum number of elements in \( X \).

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