
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
Consider and odd prime  $p$ . For each  $i$  at  $\{1, 2,..., p-1\}$ , let  $r_i$  be the rest of  $i^p$  when it is divided by  $p^2$ .
Find the sum: $r_1 + r_2 + ... + r_{p-1}$ 

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