
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
The "Nine Chapters on the Mathematical Art" is an important ancient mathematical work in China. It contains the following problem: "Now there are a fine horse and a mule that set off from Chang'an to Qi. The distance between Chang'an and Qi is 3,000 li. The fine horse travels 193 li on the first day and increases by 13 li each day. The mule travels 97 li on the first day and decreases by 0.5 li each day. After the fine horse arrives in Qi, it turns back to meet the mule. How many days later will the two meet?" The problem essentially asks to determine how many days after leaving Chang'an the two horses will meet.

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