
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 a positive integer and  $M=\{1,2,\ldots, n\}.$  A subset  $T\subset M$  is called *heavy* if each of its elements is greater or equal than  $|T|.$  Let  $f(n)$  denote the number of heavy subsets of  $M.$  Describe a method for finding  $f(n)$  and use it to calculate  $f(32).$ 

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