
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
Let \(\left\{x_{n}\right\}_{n>1}\) be the sequence of positive integers defined by \(x_{1}=2\) and \(x_{n+1} = 2x_{n}^{3} + x_{n}\) for all \(n \geq 1\). Determine the greatest power of 5 that divides the number \(x_{2014}^{2} + 1\).

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