
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
Find the greatest integer not exceeding \( 1 + \frac{1}{2^k} + \frac{1}{3^k} + \ldots + \frac{1}{N^k} \), where \( k = \frac{1982}{1983} \) and \( N = 2^{1983} \).

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