
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 book "Nine Chapters on the Mathematical Art" by Wu Jing, a seven-tiered tower is described with red lamps arranged in an increasing geometric pattern downwards, totaling 381 lamps. Calculate the number of lamps on the top of the tower.

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