
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
Alice and Bob are playing in the forest. They have six sticks of length \(1, 2, 3, 4, 5, 6\) inches. Somehow, they have managed to arrange these sticks such that they form the sides of an equiangular hexagon. Compute the sum of all possible values of the area of this hexagon.

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