
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 lined up in a row. These boxes contain balls of two colors: red and blue. Some boxes may contain only balls of one color; there are no empty boxes. It is known that the number of balls in each subsequent box (from left to right) is not less than in 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 if there are a total of 13 red and 11 blue balls in all the boxes combined?

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