
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 polar equation of line \\(C_{1}\\) is \\(\rho \sin (\theta +\dfrac{\pi }{4})=\sqrt{2}.\\) If we establish a Cartesian coordinate system \\(xOy\\) with the pole as the origin and the polar axis as the positive half-axis of \\(x\\), then the Cartesian equation of line \\(C_{1}\\) is \_\_\_\_\_; the equation of curve \\(C_{2}\\) is \\(\begin{cases} & x=\cos t, \\ & y=1+\sin t \end{cases}(t\\) as a parameter\\()), then the length of the chord cut by \\(C_{1}\\) on \\(C_{2}\\) is \_\_\_.

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