
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  $n$  be a positive integer. Jadzia has to write all integers from  $1$  to  $2n-1$  on a board, and she writes each integer  in blue or red color. We say that pair of numbers  $i,j\in \{1,2,3,...,2n-1\}$ , where  $i\leqslant j$ , is  $\textit{good}$  if and only if number of blue numbers among  $i,i+1,...,j$  is odd. Determine, in terms of  $n$ , maximal number of good pairs.

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