
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 brother and sister are dividing a triangular cake in the following way: the brother indicates a point on the cake, and the sister makes a straight-line cut through this point and chooses a piece for herself. Each of them wants to get the largest possible piece. Where should the brother place the point? What portion of the cake will each of them receive in this case?

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