
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) Write down all the permutations of the elements 1, 2, 3, 4 in this unusual arrangement!

b) What is the rank of the permutation 5341726 of the elements 1, 2, 3, 4, 5, 6, 7

I. in this unusual arrangement?

II. in the usual arrangement?

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