
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
In the right triangle \(ABC\), \(\angle C\) is a right angle, and the side \(CA = 4\). On the leg \(BC\) there is a point \(D\), such that \(CD = 1\). A circle with radius \(\frac{\sqrt{5}}{2}\) passes through the points \(C\) and \(D\) and is tangent at point \(C\) to the circle circumscribed around the triangle \(ABC\). Find the area of triangle \(ABC\).

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