
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
How many SDRs (System of Distinct Representatives) does the following array have?
$$
\begin{array}{ccccccccccc}
1 & 2 & 3 & 4 & 5 & 6 & \cdots & n-2 & n-1 & n & \\
2 & 3 & 1 & 5 & 6 & 7 & \cdots & n-1 & n & 4 & (n \geqslant 6) \\
3 & 1 & 2 & 6 & 7 & 8 & \cdots & n & 4 & 5 &
\end{array}
$$

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