
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  $n\geq 2$  be a positive integer and let  $a_1,a_2,...,a_n\in[0,1]$  be real numbers. Find the maximum value of the smallest of the numbers: \[a_1-a_1a_2, \ a_2-a_2a_3,...,a_n-a_na_1.\]

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