
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 polar coordinate system, the curve C is given by $\rho\cos(\theta + \frac{\pi}{4}) = 1$. A ray is drawn from the pole O to intersect with the curve C at point Q. A point P is chosen on the ray OQ such that $|OP| \cdot |OQ| = \sqrt{2}$.
(1) Find the polar equation of the trajectory C1 for point P.
(2) Establish a Cartesian coordinate system xOy with the pole O as the origin and the polar axis as the positive x-axis. If the line $l: y = -\sqrt{3}x$ intersects curve C1 at point E (distinct from O) and intersects curve C2 described by the parametric equations $\begin{cases} x=\frac{1}{2} - \frac{\sqrt{2}}{2}t \\ y=\frac{\sqrt{2}}{2}t \end{cases}$ (with t as the parameter) at point F, find the length of |EF|.

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