
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  $p$  be a prime number, and define a sequence by:  $x_i=i$  for  $i=,0,1,2...,p-1$  and  $x_n=x_{n-1}+x_{n-p}$  for  $n \geq p$ 
Find the remainder when  $x_{p^3}$  is divided by  $p$ .

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