
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 the ancient Chinese mathematical classic "Jiuzhang Suanshu," there is a passage describing a scenario: There are a good horse and a mediocre horse traveling from Chang'an to Qi, a distance of 1125 li. The good horse travels 103 li on the first day and increases its distance by 13 li each day; the mediocre horse travels 97 li on the first day and decreases its distance by half a li each day. The good horse reaches Qi first and then turns back to meet the mediocre horse. They meet after a certain number of days. The question is: How many days do they meet after?

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