
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
The number of positive integer pairs  $(a,b)$  that have  $a$  dividing  $b$  and  $b$  dividing  $2013^{2014}$  can be written as  $2013n+k$ , where  $n$  and  $k$  are integers and  $0\leq k<2013$ .  What is  $k$ ?  Recall  $2013=3\cdot 11\cdot 61$ .

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