
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
Given that Liu Bei and Guan Yu meet at the midpoint between the long and short pavilions two hours after Liu Bei starts chasing Guan Yu, and that Guan Yu had turned back and headed towards the long pavilion after he reached the short pavilion, calculate the ratio of Liu Bei's speed to Guan Yu's speed.

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