
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
From the numbers $1, 2, \ldots, n$, we want to select sets of three numbers $\{a, b, c\}$ such that $a < b < c$, with the additional condition that for any two selected sets $\{a, b, c\}$ and $\{a', b', c'\}$, at most one of the equalities $a = a'$, $b = b'$, and $c = c'$ can hold.

What is the maximum number of such sets of three numbers that we can select?

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