
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 net for hexagonal pyramid is constructed by placing a triangle with side lengths  $x$ ,  $x$ , and  $y$  on each side of a regular hexagon with side length  $y$ . What is the maximum volume of the pyramid formed by the net if  $x+y=20$ ?

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