
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 of  $\{1, 2, \dots, 7\}$  is chosen uniformly at random. A partition of the permutation into contiguous blocks is correct if, when each block is sorted independently, the entire permutation becomes sorted. For example, the permutation  $(3, 4, 2, 1, 6, 5, 7)$  can be partitioned correctly into the blocks  $[3, 4, 2, 1]$  and  $[6, 5, 7]$ , since when these blocks are sorted, the permutation becomes  $(1, 2, 3, 4, 5, 6, 7)$ . Find the expected value of the maximum number of blocks into which the permutation can be partioned correctly. 

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