
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
Your math friend Steven rolls five fair icosahedral dice (each of which is labelled  $1,2, \dots,20$  on its sides). He conceals the results but tells you that at least half the rolls are  $20$ . Suspicious, you examine the first two dice and find that they show  $20$  and  $19$  in that order. Assuming that Steven is truthful, what is the probability that all three remaining concealed dice show  $20$ ?

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