
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 n be an odd positive integer.Let M be a set of  $n$  positive integers ,which are 2x2 different. A set  $T$   $\in$   $M$  is called "good" if the product of its elements is divisible by the sum of the elements in  $M$ , but is not divisible by the square of the same sum. Given that  $M$  is "good",how many "good" subsets of  $M$  can there be?

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