
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  $ x \minus{} y$  plane, find the area of the region bounded by the parameterized curve as follows.

 $ \left\{\begin{array}{ll} x \equal{} \cos 2t & \quad 
y \equal{} t\sin t & \quad \end{array} \right.\ (0\leq t\leq 2\pi)$ 

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