
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 \(xOy\), consider two circles centered at the origin \(O\) with radii \(a\) and \(b\) respectively where \(a > b > 0\). Point \(Q\) is the intersection of the larger circle's radius \(OP\) with the smaller circle. Draw \(AN\) perpendicular to \(Ox\) with foot at \(N\) passing through point \(P\), and draw \(QM\) perpendicular to \(PN\) with foot at \(M\) passing through point \(Q\). When the radius \(OP\) rotates around point \(O\), trace the trajectory of point \(M\) to form curve \(E\).

(1) Find the equation of curve \(E\);

(2) Given three points \(A\), \(B\), and \(C\) on curve \(E\) such that \(\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}=\overrightarrow{0}\), determine the area of triangle \(\triangle ABC\).

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