
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 subtraction pyramid is a pyramid composed of non-negative integers, each of which is the difference of two closest numbers from the previous level (read from the bottom up). Here is an example of a subtraction pyramid:

    1
    2
    2
    5 7
    4
    3
    5
    8

A significant number is the largest number in the subtraction pyramid. An excellent pyramid is a subtraction pyramid that has 0 at the top and at least one level consisting of distinct numbers.

1. How many levels must the excellent pyramid have at least?
2. What is the smallest significant number that can be included in the excellent pyramid with the minimum number of levels?

(Hint: What does the level below the top look like?)

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