
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 bag contains 5 white, 5 black, and 2 blue balls. What is the minimum number of balls that need to be taken out (without looking into the bag) to ensure that there are at least three balls of the same color among them?

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