
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
Define the sequence \(\left\{x_{i}\right\}_{i \geq 0}\) by \(x_{0}=x_{1}=x_{2}=1\) and \(x_{k}=\frac{x_{k-1}+x_{k-2}+1}{x_{k-3}}\) for \(k>2\). Find \(x_{2013}\).

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