
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
The number 15 is written on a blackboard. A move consists of erasing the number x and replacing it with x+y where y is a randomly chosen number between 1 and 5 (inclusive). The game ends when the number on the blackboard exceeds 51. Calculate the expected value of the number on the blackboard at the end of the game.

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