
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
Scott stacks golfballs to make a pyramid. The first layer, or base, of the pyramid is a square of golfballs and rests on a flat table. Each golfball, above the first layer, rests in a pocket formed by four golfballs in the layer below. Each layer, including the first layer, is completely filled. The four triangular faces of the pyramid include a total of exactly 145 different golfballs. How many layers does this pyramid have?

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