
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
An isosceles right triangle \(ABC\) has an area of 1. Points \(D, E, F\) are chosen on \(BC\), \(CA\), and \(AB\) respectively such that \(\triangle DEF\) is also an isosceles right triangle. Find the smallest possible area of \(\triangle DEF\).

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