
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

The leader of an IMO team chooses positive integers \(n\) and \(k\) with \(n > k\), and announces them to the deputy leader and a contestant. The leader then secretly tells the deputy leader an \(n\)-digit binary string, and the deputy leader writes down all \(n\)-digit binary strings which differ from the leader's in exactly \(k\) positions. The contestant is allowed to look at the strings written by the deputy leader and guess the leader's string. What is the minimum number of guesses (in terms of \(n\) and \(k\)) needed to guarantee the correct answer?

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