
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 parametric equation of the line \(l\) is given by \(\begin{cases} x=t \\ y=1+2t \end{cases}\) (where \(t\) is the parameter). Using \(O\) as the pole and the positive \(x\)-axis as the initial ray, a polar coordinate system is established. The polar equation of curve \(C\) is given by \(ρ=2\sqrt{2}\sin\left(θ+\frac{π}{4}\right)\).
(1) Write the standard equation of line \(l\) and the Cartesian equation of curve \(C\);
(2) If the line \(θ=α\) intersects curve \(C\) at points \(O\) and \(P\), and the line \(θ=α+\frac{π}{2}\) intersects curve \(C\) at points \(O\) and \(Q\), and if line \(PQ\) is perpendicular to line \(l\), determine the coordinates of the intersection point of line \(PQ\) and \(l\).

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