
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  $(x_n)$  be a sequence of positive integers defined by  $x_1=2$  and  $x_{n+1}=2x_n^3+x_n$  for all integers  $n\ge1$ . Determine the largest power of  $5$  that divides  $x_{2014}^2+1$ .

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