
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
Six people, all of different weights, are trying to build a human pyramid:
$$
\begin{array}{c}
\text{A} \\
\text{B C} \\
\text{D E F}
\end{array}
$$

We say that someone not in the bottom row is "supported by" each of the two closest people beneath them. How many different pyramids are possible if nobody can be supported by anybody of lower weight?

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