
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
Find the number of permutations $\left(a_{1}, a_{2}, \ldots, a_{6}\right)$ of $(1, 2, 3, 4, 5, 6)$ such that the minimal number of transpositions required to transform $\left(a_{1}, \ldots, a_{6}\right)$ into $(1, \ldots, 6)$ is 4.

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