
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
Given a positive integer $\mathrm{n}$, write the $\mathrm{n}$ positive integers $1, 2, \ldots, \mathrm{n}$ on paper, where some numbers are written in red and some in blue, with both colors used, and each number is only written in one color. For $1 \leq i \leq j \leq n$, if there are an odd number of blue numbers among $i, i+1, \ldots, j$, then the pair of numbers $(i, j)$ is called "good." Find the maximum possible number of good pairs.

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