
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
Consider the ellipse  $E: 3x^2+y^2=3$  and the hyperbola  $H: xy=\frac 34.$ (1) Find all points of intersection of  $E$  and  $H$ .

(2) Find the area of the region expressed by the system of inequality
\[\left\{
\begin{array}{ll}
3x^2+y^2\leq 3 &\quad  
xy\geq \frac 34 , &\quad
\end{array}
\right.\]

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