
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
Let \(ABC\) be a triangle with area 1. Let points \(D\) and \(E\) lie on \(AB\) and \(AC\), respectively, such that \(DE\) is parallel to \(BC\) and \(\frac{DE}{BC} = \frac{1}{3}\). If \(F\) is the reflection of \(A\) across \(DE\), find the area of triangle \(FBC\).

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