
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 a Cartesian coordinate system \\(xOy\\) is established with the pole as the origin and the positive half-axis of the polar axis as the \\(x\\)-axis, then the Cartesian equation of line \\(C_{1}\\) is \_\_\_\_\_\_; the equation of curve \\(C_{2}\\) is \\( \begin{cases} \overset{x=\cos t}{y=1+\sin t}\end{cases} \\) (where \\(t\\) is 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}
user