
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
The area of the largest regular hexagon that can fit inside a rectangle with side lengths 20 and 22 can be expressed as \( a \sqrt{b} - c \), for positive integers \( a \), \( b \), and \( c \), where \( b \) is squarefree. Compute \( 100a + 10b + c \).

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