
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
In the sequence \(\left\{a_{n}\right\}\), for \(1 \leqslant n \leqslant 5\), we have \(a_{n}=n^{2}\). Additionally, for all positive integers \(n\), the following holds:
\[ a_{n+5} + a_{n+1} = a_{n+4} + a_{n}. \]
Determine the value of \(a_{2023}\).

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