
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  $A$  be a set of numbers chosen from  $1,2,..., 2015$  with the property that any two distinct numbers, say  $x$  and  $y$ , in  $A$  determine a unique isosceles triangle (which is non equilateral) whose sides are of length  $x$  or  $y$ . What is the largest possible size of  $A$ ?

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