
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 10 boxes in a row. Each of these boxes contains red and blue balls. Some of the boxes may contain balls of a single color; there are no empty boxes. It is known that each subsequent box (from left to right) contains at least as many balls as the previous one. It is also known that no two boxes have the same combination of red and blue balls. How many blue and how many red balls are in the rightmost box, given that there are a total of 11 red and 13 blue balls in all the boxes combined?

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