
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
Given a permutation  $(a_{1}, a_{1},...,a_{n})$  of the numbers  $1, 2,...,n$  one may interchange any two consecutive "blocks" - that is, one may transform 
( $a_{1}, a_{2},...,a_{i}$ , $\underbrace {a_{i+1},... a_{i+p},}_{A} $   $ \underbrace{a_{i+p+1},...,a_{i+q},}_{B}...,a_{n}) $ into  $ (a_{1}, a_{2},...,a_{i},$   $ \underbrace {a_{i+p+1},...,a_{i+q},}_{B} $   $ \underbrace {a_{i+1},... a_{i+p}}_{A}$  $,...,a_{n}) $ by interchanging the "blocks"  $A$  and  $B$ . Find the least number of such changes which are needed to transform  $(n, n-1,...,1)$  into  $(1,2,...,n)$ 

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