
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
Given a sequence of positive integers \(\{y_{n}\}\) satisfying
\[
y_{n+2} = \frac{y_{n} + 2013}{1 + y_{n+1}} \quad (n \geq 1),
\]
find the minimum value of \(y_{1} + y_{2}\).

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