
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. Determine the smallest integer $N$ which is divisible by $p$ such that when $N$ is divided by any integer $n$ less than $p$,

1. the remainder is $n-1$
2. the remainder is 1.

For example, if $p=11$.

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