
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
A problem from the "Nine Chapters on the Mathematical Art" states: A fine horse and a mule travel from Luoyang to Qi. The distance from Qi to Luoyang is 1,125 li. The fine horse travels 103 li on the first day and increases by 13 li each day. The mule travels 97 li on the first day and decreases by half a li each day. The fine horse arrives in Qi first and then turns back to meet the mule. The question is: How many days does it take for the two animals to meet?

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