
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 player starts with \( A \) blue cards, \( B \) red cards, and \( C \) white cards. He scores points as he plays each card. If he plays a blue card, his score is the number of white cards remaining in his hand. If he plays a red card, his score is three times the number of blue cards remaining in his hand. If he plays a white card, his score is twice the number of red cards remaining in his hand. What is the lowest possible score as a function of \( A \), \( B \), and \( C \), and how many different ways can it be achieved?

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