
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
We define the sets  $A_1,A_2,...,A_{160}$  such that  $\left|A_{i} \right|=i$  for all  $i=1,2,...,160$ . With the elements of these sets we create new sets  $M_1,M_2,...M_n$  by the following procedure: in the first step we choose some of the sets  $A_1,A_2,...,A_{160}$  and we remove from each of them the same number of elements. These elements that we removed are the elements of  $M_1$ . In the second step we repeat the same procedure in the sets that came of the implementation of the first step and so we define  $M_2$ . We continue similarly until there are no more elements in  $A_1,A_2,...,A_{160}$ , thus defining the sets  $M_1,M_2,...,M_n$ . Find the minimum value of  $n$ .

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