
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 ancient Chinese mathematical text "Suan Shu Tong Zong" states: "Three hundred and seventy-eight miles to the gate, initially the journey is easy, but the next day, due to foot pain, the distance is reduced by half, and it takes six mornings to reach the gate..." The essence of the problem is: "A person starts from a point three hundred and seventy-eight miles away from the gate. On the first day, the journey is easy. From the second day onwards, due to foot pain, the distance covered each day is half of the previous day. It takes six days in total to reach the gate..." The question is, how far did the person walk on the first day?

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