
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
There is an L-shaped cake as shown in the diagram. We are required to cut it into three parts using a single cut, only in the manner depicted in the diagram (not cutting diagonally or horizontally). To maximize the area of the smallest piece, what is the maximum possible area of this smallest piece in square centimeters?

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