
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 $xOy$, with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_{1}$ is $\rho\sin (\theta+ \frac {\pi}{4})= \frac { \sqrt {2}}{2}a$, and the parametric equation of curve $C_{2}$ is $\begin{cases} x=-1+\cos \theta \\ y=-1+\sin \theta\end{cases}$ (where $\theta$ is the parameter).

(Ⅰ) Find the Cartesian coordinate equation of $C_{1}$;

(Ⅱ) When $C_{1}$ and $C_{2}$ have two common points, find the range of values for the real number $a$.

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