
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
Given triangles \(ABC\) and \(A'B'C'\) with areas of 1 and 2025, respectively. It is known that rays \(AB\) and \(A'B'\) are parallel and go in opposite directions. The same is true for pairs \(BC\) and \(B'C'\), \(CA\) and \(C'A'\). Let \(A''\), \(B''\), and \(C''\) be the midpoints of segments \(AA'\), \(BB'\), and \(CC'\). Find the area of triangle \(A''B''C''\).

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