
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 \(A, B, C,\) and \(D\) are points on a circle with radius 1, \(\overrightarrow{AB} + 2 \overrightarrow{AC} = \overrightarrow{AD}\), and \(|AC| = 1\). Find the area of the quadrilateral \(ABDC\).

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