
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 line parallel to the hypotenuse \( AB \) of the right triangle \( ABC \) intersects the leg \( AC \) at point \( D \) and the leg \( BC \) at point \( E \), with \( DE = 2 \) and \( BE = 1 \). A point \( F \) is taken on the hypotenuse such that \( BF = 1 \). It is also known that \(\angle FCB = \alpha\). Find the area of triangle \( ABC \).

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