
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
Ben is throwing darts at a circular target with diameter 10.  Ben never misses the target when he throws a dart, but he is equally likely to hit any point on the target.  Ben gets  $\lceil 5-x \rceil$  points for having the dart land  $x$  units away from the center of the target.  What is the expected number of points that Ben can earn from throwing a single dart?  (Note that  $\lceil y \rceil$  denotes the smallest integer greater than or equal to  $y$ .)

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