
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
Let \( S = \{1, 2, \cdots, 11\} \). For each 7-element subset of \( S \), arrange these seven numbers in ascending order and take the middle number. What is the sum of all the middle numbers taken from each subset?

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