
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
Honza had 100 identical jars, which he used to build triangular pyramids. The top level of the pyramid always has one jar, the second level from the top represents an equilateral triangle whose side consists of two jars, and so on. Here is an example construction of a three-level pyramid:

1. How many jars did Honza need for a five-level pyramid?
2. How many levels did the pyramid have, for which most of Honza's jars were used?

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