
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 sequence \(\left(a_{n}\right)\) is defined such that \(a_{n}=n^{2}\) for \(1 \leq n \leq 5\) and for all natural numbers \(n\) the following equality holds: \(a_{n+5} + a_{n+1} = a_{n+4} + a_{n}\). Find \(a_{2015}\).

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