
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  $n,k$  be positive integers so that  $n \ge k$ .Find the maximum number of binary sequances of length  $n$  so that fixing any arbitary  $k$  bits they do not produce all binary sequances of length  $k$ .For exmple if  $k=1$  we can only have one sequance otherwise they will differ in at least one bit which means that bit produces all binary sequances of length  $1$ .

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