
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 re-evaluation of the Council of Wise Men occurs as follows: the king lines them up in a single file and places a hat of either white, blue, or red color on each of their heads. All wise men can see the colors of the hats of everyone in front of them, but they cannot see their own hat or the hats of those behind them. Once per minute, each wise man must shout out one of the three colors (each wise man shouts out a color only once).

After this process is completed, the king will execute any wise man who shouts a color different from the color of his own hat.

The night before the re-evaluation, all one hundred members of the Council of Wise Men agreed and came up with a strategy to minimize the number of those executed. How many of them are guaranteed to avoid execution?

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