
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
A king has eight sons, and they are all fools. Each night, the king sends three of them to guard the golden apples from the Firebird. The princes cannot catch the Firebird and blame each other, so no two of them agree to go on guard together a second time. What is the maximum number of nights this can continue?

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