
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 Cartesian coordinate system \( xoy \), the curve \( C \) is defined by the parametric equations 
\[
\begin{cases} 
x = 4t^2 \\ 
y = 4t 
\end{cases} \quad (t \text{ is the parameter})
\]
Establish a polar coordinate system with \( O \) as the pole and the positive half of the \( x \)-axis as the polar axis. The polar equation of line \( l \) is \( \rho(\cos \theta - \sin \theta) = 4 \), and it intersects curve \( C \) at points \( A \) and \( B \).
  1. Find the standard equations of curve \( C \) and line \( l \) in the Cartesian coordinate system.
  2. Calculate the area of triangle \( \triangle AOB \).

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