
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, given the curve $C:\\rho \\cos (\\theta +\\dfrac{\\pi }{4})=1$, a line is drawn through the pole $O$ intersecting the curve $C$ at point $Q$. On $OQ$, a point $P$ is chosen such that $| OP |\\cdot | OQ |=\\sqrt{2}.$

(1) Find the polar coordinate equation of the trajectory of point $P$ (${{C}\_{1}}$);

(2) Establish a rectangular coordinate system $xOy$ with the pole as the origin and the polar axis as the positive semi-axis of $x$. If the line $l:y=-\\sqrt{3}x$ intersects the curve (${{C}\_{1}}$) from part (1) at $E$ (distinct from $O$) and intersects the curve ${{C}\_{2}:\\left\\{\\begin{matrix}x= \\dfrac{1}{2}- \\dfrac{ \\sqrt{2}}{2}t \\\\ y= \\dfrac{ \\sqrt{2}}{2}t\\end{matrix}(t\\text{ is a parameter})\\right., \\}$ at $F$, find the value of $| EF |$.

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