
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 triangle  $ABC$  with area  $1$  is given. Anja and Bernd are playing the following game: Anja chooses a point  $X$  on side  $BC$ . Then Bernd chooses a point  $Y$  on side  $CA$  und at last Anja chooses a point  $Z$  on side  $AB$ . Also,  $X,Y$  and  $Z$  cannot be a vertex of triangle  $ABC$ . Anja wants to maximize the area of triangle  $XYZ$  and Bernd wants to minimize that area.
What is the area of triangle  $XYZ$  at the end of the game, if both play optimally?

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