
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 container holds $26$ orange balls, $21$ purple balls, $20$ brown balls, $15$ gray balls, $12$ silver balls, and $10$ golden balls. Calculate the minimum number of balls that must be drawn from the container without replacement to ensure that at least $17$ balls of one color are retrieved.

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