
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 king decided to test his one hundred wise men by conducting the following experiment: he will line them up with their eyes blindfolded, then place a black or white cap on each of their heads. After the blindfolds are removed, each wise man, starting from the last in the line, must state the color of his cap. If he guesses incorrectly, he will be executed. The wise men have some time to strategize before the test. How many wise men are guaranteed to be saved?

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