
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 bottom layer of the tower has 13 times as many lamps as the top layer. Let x be the number of lamps on the top layer. Then, the bottom layer has 13x lamps. Each adjacent lower layer has one less n than the layer above it. The total number of lamps in the tower is the sum of the lamp count for each layer from top to bottom, which can be expressed as an arithmetic series. The sum of the lamps is 126, so we can set up the equation: x + (x + n) + (x + 2n) + ... + (x + 8n) = 126.

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