
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
There are 127 balls in a row, each of which is either red, green, or blue. It is known that:

- There is at least one red, one green, and one blue ball.
- To the left of each blue ball, there is a red ball.
- To the right of each green ball, there is a red ball.

(a) What is the maximum number of red balls that can lie in the row?

(b) What is the minimum number of red balls that can lie in the row?

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