
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 \( F \) be the set of all ordered \( n \)-tuples \(\left(A_{1}, A_{2}, \cdots, A_{n}\right)\), where \( A_{i} \) (for \( 1 \leq i \leq n \)) are subsets of \(\{1, 2, \cdots, 1998\}\). Find \(\sum_{\left(A_{1}, A_{2}, \cdots, A_{n}\right) \in F} \left| A_{1} \cup A_{2} \cup \cdots \cup A_{n} \right|\).

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