
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
Darryl has a six-sided die with faces  $1, 2, 3, 4, 5, 6$ . He knows the die is weighted so that one face
comes up with probability  $1/2$  and the other five faces have equal probability of coming up. He
unfortunately does not know which side is weighted, but he knows each face is equally likely
to be the weighted one. He rolls the die  $5$  times and gets a  $1, 2, 3, 4$  and  $5$  in some unspecified
order. Compute the probability that his next roll is a  $6$ .

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