
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
In a permutation \((x_{1}, x_{2}, \ldots, x_{n})\) of the set \(\{1, 2, \ldots, n\}\), a pair \((x_{i}, x_{j})\) is called discordant if \(i < j\) and \(x_{i} > x_{j}\). Let \(d(n, k)\) be the number of such permutations with exactly \(k\) discordant pairs. Find \(d(n, 2)\) and \(d(n, 3)\).

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