
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 that the line $$\begin{cases} \left.\begin{matrix}x=1+t \\ y=4-2t\end{matrix}\right.\end{cases}$$ (where $t\in\mathbb{R}$) intersects with the circle $$\begin{cases} \left.\begin{matrix}x=2\cos\theta+2 \\ y=2\sin\theta\end{matrix}\right.\end{cases}$$ (where $\theta\in[0,2\pi]$) at points A and B, compute the area of the circle whose diameter is AB.

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