
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
In Happy City there are  $2014$  citizens called  $A_1, A_2, \dots , A_{2014}$ . Each of them is either *happy* or *unhappy* at any moment in time. The mood of any citizen  $A$  changes (from being unhappy to being happy or vice versa) if and only if some other happy citizen smiles at  $A$ . On Monday morning there were  $N$  happy citizens in the city.

The following happened on Monday during the day: the citizen  $A_1$  smiled at citizen  $A_2$ , then  $A_2$  smiled at  $A_3$ , etc., and, finally,  $A_{2013}$  smiled at  $A_{2014}$ . Nobody smiled at anyone else apart from this. Exactly the same repeated on Tuesday, Wednesday and Thursday. There were exactly  $2000$  happy citizens on Thursday evening.

Determine the largest possible value of  $N$ .

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