
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 fraction  $\tfrac1{2015}$  has a unique "(restricted) partial fraction decomposition'' of the form \[\dfrac1{2015}=\dfrac a5+\dfrac b{13}+\dfrac c{31},\] where  $a$ ,  $b$ , and  $c$  are integers with  $0\leq a<5$  and  $0\leq b<13$ .  Find  $a+b$ .

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