
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
A game has the following rules: There are 5 red balls and 5 yellow balls in a pocket. You draw 5 balls at a time. If all 5 balls are the same color, you get 100 points. If 4 of the balls are the same color and 1 is different, you get 50 points. Otherwise, you get no points. What is the expected score when Zhang draws balls once?

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