
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 red and 10 yellow apples with a total weight of 1 kg. It is known that the weights of any two apples of the same color differ by no more than 40 grams. All apples were paired "red with yellow" in sequence, with the red apples chosen in non-decreasing order and the yellow apples in non-increasing order (i.e., the heaviest red was paired with the lightest yellow, the second heaviest red with the lightest of the remaining yellows, and so on). What is the maximum possible weight of a pair?

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