
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  $n$  to be a positive integer. A family  $\wp$  of intervals  $[i, j]$  with  $0 \le i < j \le n$  and  $i$ ,  $j$  integers is considered *happy* if, for any  $I_1 = [i_1, j_1] \in \wp$  and  $I_2 = [i_2, j_2] \in \wp$  such that  $I_1 \subset I_2$ , we have  $i_1 = i_2$  **or**  $j_1 = j_2$ . 

Determine the maximum number of elements of a *happy* family.

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