
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 $(xOy)$, the parametric equation of circle $C$ is given by $\begin{cases} x=a+\cos \theta \ y=\sin \theta \end{cases}$ $(\theta$ is the parameter$)$. Establish a polar coordinate system with the coordinate origin as the pole and the non-negative semi-axis of $x$ as the polar axis. The polar equation of line $l$ is $\rho\sin (\theta- \frac {π}{4})= \frac { \sqrt {2}}{2}$. If line $l$ is tangent to circle $C$, then the real number $a=$ _____ .

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