
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. These boxes contain balls of two colors: red and blue. Some of the boxes may have balls of only one color; there are no empty boxes. It is known that each subsequent box (from left to right) has 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, if there are a total of 10 red and 14 blue balls in all the boxes?

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