
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 work "The Compendious Book on Calculation by Completion and Balancing," there is a passage that reads: "Three hundred and seventy-eight miles to the pass, the first day's journey is not difficult, the next day the pain in the feet is halved, and after six days, one finally reaches the pass." The essence of this passage is: a person needs to reach a certain pass, which is $378$ miles away. They walk briskly on the first day, and starting from the second day, due to foot pain, they walk half the distance of the previous day. It takes a total of six days to reach the destination. What is the distance this person walked on the third day?

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