
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 \( S = \{1, 2, 3, \ldots, 1990\} \), and let \( A \subset S \) with \( |A| = 26 \). If the sum of all elements in \( A \) is a multiple of 5, then \( A \) is called a "good subset" of 26 elements of \( S \). Find the number of "good subsets" of 26 elements of \( S \).

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