
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
A natural number $N$ leaves a remainder of 8 when divided by 9, a remainder of 7 when divided by 8, a remainder of 6 when divided by 7, a remainder of 5 when divided by 6, a remainder of 4 when divided by 5, a remainder of 3 when divided by 4, a remainder of 2 when divided by 3, and a remainder of 1 when divided by 2. Find the smallest value of $N$.

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