
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
A permutation  $a_1,a_2,\cdots ,a_6$  of numbers  $1,2,\cdots ,6$  can be transformed to  $1,2,\cdots,6$  by transposing two numbers exactly four times. Find the number of such permutations.

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