
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 set of  $n$  standard dice are shaken and randomly placed in a straight line. If  $n < 2r$  and  $r < s$ , then the probability that there will be a string of at least  $r$ , but not more than  $s$ , consecutive  $1$ 's can be written as  $\frac{P}{6^{s+2}}$ . Find an explicit expression for  $P$ .

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