
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
Find the maximal possible  $n$ , where  $A_1, \dots, A_n \subseteq \{1, 2, \dots, 2016\}$  satisfy the following properties. 
- For each  $1 \le i \le n$ ,  $\lvert A_i \rvert = 4$ .
- For each  $1 \le i < j \le n$ ,  $\lvert A_i \cap A_j \rvert$  is even. 

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