
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 \(\frac{1}{2015}\) has a unique "(restricted) partial fraction decomposition" of the form
\[ \frac{1}{2015}=\frac{a}{5}+\frac{b}{13}+\frac{c}{31}, \]
where \(a, b, c\) 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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