
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
In our daily life, for a pair of new bicycle tires, the rear tire wears out faster than the front tire. Through testing, it is found that the front tire of a general bicycle is scrapped after traveling 11,000 kilometers, while the rear tire is scrapped after traveling 9,000 kilometers. It is evident that when the rear tire is scrapped after traveling 9,000 kilometers, the front tire can still be used, which inevitably leads to a certain waste. If the front and rear tires are swapped once, allowing the front and rear tires to be scrapped simultaneously, the bicycle can travel a longer distance. How many kilometers can the bicycle travel at most after swapping once? And after how many kilometers should the front and rear tires be swapped?

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