
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
In RNG baseball, a team of infinitely many people play on a square field, with a base at each vertex; in particular, one of the bases is called the home base. Every turn, a new player stands at home base and chooses a number \( n \) uniformly at random from \(\{0,1,2,3,4\}\). Then, the following occurs:
- If \( n > 0 \), then the player and everyone else currently on the field moves (counterclockwise) around the square by \( n \) bases. However, if in doing so a player returns to or moves past the home base, he/she leaves the field immediately and the team scores one point.
- If \( n = 0 \) (a strikeout), then the game ends immediately; the team does not score any more points.

What is the expected number of points that a given team will score in this game?

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