
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
Two boxes contain colored balls. Box 1 has $40$ red balls, $30$ green balls, $25$ yellow balls, and $15$ blue balls. Box 2 has $35$ red balls, $25$ green balls, and $20$ yellow balls. Find the minimum number of balls that must be drawn from these boxes (without replacement, drawing from any box at will) to guarantee that at least $20$ balls of a single color are drawn.

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