
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
After Liu Xiang, a famous Chinese track and field athlete, set a new world record of 12.88 seconds in the 110m hurdles, a group of experts analyzed the images and data from his races and training sessions by inputting them into a computer. The analysis showed that the time taken to clear each hurdle (the "hurdle cycle" time between two adjacent hurdles) never exceeded one second, with the fastest "hurdle cycle" reaching an astonishing 0.96 seconds. The distance from the starting line to the first hurdle is 13.72 meters, and Liu Xiang's best time for this segment is 2.5 seconds. The distance from the last hurdle to the finish line is 14.02 meters, with Liu Xiang's best time for this segment being 1.4 seconds. Based on the above data, calculate the distance between two adjacent hurdles in seconds, and theoretically, the best time Liu Xiang could achieve in the 110m hurdles.

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