
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
Students in a school are arranged in an order that when you count from left to right, there will be  $n$  students in the first row,  $n-1$  students in the second row,  $n - 2$  students in the third row,... until there is one student in the  $n$ th row. All the students face to the first row. For example, here is an arrangement for  $n = 5$ , where each  $*$  represents one student: $*$  $* *$  $* * *$  $* * * *$  $* * * * *$  (first row)

Each student will pick one of two following statement (except the student standing at the beginning of the row):
i) The guy before me is telling the truth, while the guy standing next to him on the left is lying.
ii) The guy before me is lying, while the guy standing next to him on the left is telling the truth.

For  $n = 2015$ , find the maximum number of students telling the truth. 
(A student is lying if what he said is not true. Otherwise, he is telling the truth.)

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