
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 a circle \\(x^{2}+y^{2}-2x=0\\) with center \\(C\\), and a line \\( \begin{cases} x=-1+ \dfrac { \sqrt {2}}{2}t \\\\ y=3- \dfrac { \sqrt {2}}{2}t\end{cases}\\) (where \\(t\\) is a parameter) intersects the circle at points \\(A\\) and \\(B\\), then the area of \\(\triangle ABC\\) is \_\_\_\_\_\_.

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