
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
Consider a random permutation of the set  $\{1, 2, . . . , 2015\}$ . In other words, for each  $1 \le i \le 2015$ ,  $i$  is sent to the element  $a_i$  where  $a_i \in \{1, 2, . . . , 2015\}$  and if  $i \neq j$ , then  $a_i \neq a_j$ . What is the expected number of ordered pairs  $(a_i, a_j )$  with  $i - j > 155$  and  $a_i - a_j > 266$ ?


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